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In a speech in London, Mr Corbyn said: "We, the Labour Party, are overwhelmingly for staying in, because we believe the European Union has brought investment, jobs and protection for workers, consumers and the environment.
"But also because we recognise that our membership offers a crucial route to meeting the challenges we face in the 21st century, on climate change, on restraining the power of global corporations and ensuring they pay fair taxes, on tackling cyber-crime and terrorism, on ensuring trade is fair with protections for workers and consumers and in addressing refugee movements."
Analysis: John Pienaar, BBC deputy political editor
Mutinous grumbling among backbenchers has become part of the background noise to all Labour Party politics at Westminster, constant as the song of crickets on a warm summer evening and, so far, about as harmless to the leader many of them privately despise.
If this referendum ends in the momentous outcome of a vote to leave - and that is perfectly possible - and Labour MPs at Westminster are left asking themselves and each other who is to blame, many of them will cast wrathful glances in the direction of their leader.
But will their public and private rebukes be fair?
Labour had a "distinct agenda" from that of the government, which also backs Remain, he said.
He criticised media coverage and warnings made by both sides of the debate, saying it had been dominated too much by "myth-making and prophecies of doom".
Responding to criticism that his campaigning was half-hearted, Mr Corbyn listed the cities he was due to visit, said there were no "no go areas" and insisted that the intensity of Labour's campaigning would grow as polling day gets nearer.
"I don't think anyone is going to be in any doubt what our views are come 23 June... we are getting our message out," he said.
There are just weeks to go until the UK decides on its future in the European Union, in the in-out referendum on 23 June.
The Remain campaign believes that securing the support of Labour voters will be vital to winning the referendum.
Work and pay
How working conditions and pay rates are affected by EU membership.
What the leave and remain sides are saying about work and pay in the #EUref campaign
Unemployment is over 10% in the EU, almost double the rate in the UK
Some workers’ rights are guaranteed by EU laws but tax rates, benefits and the minimum wage are down to UK government decisions
Less regulation in the workplace would create more jobs
Maternity leave and holiday pay would only change if Britain decided to change them
The UK could get more investment from countries outside the EU
Lower migration would push wages up
Three million jobs in the UK are linked to trade with the EU
The EU has delivered guaranteed holiday pay, paid maternity leave, and increased protection in the workplace
The UK gets £66m investment every day from the EU
EU referendum issues guide: Explore the argumentshttp://www.bbc.co.uk/news/uk-politics-eu-referendum-36027205http://www.bbc.co.uk/news/special/2016/newsspec_13606/content/iframe/english/index.inc.app.htmlExplore all the issuesChoose an issue:What both sides are sayingAll issuesMain viewsShare this pageEU referendum issues guideWhat the leave and remain sides are saying in the #EUref campaign
But there have been anxieties within the Remain camp that Labour voters might not turn out to vote - in a close contest levels of turnout can be decisive.
In an interview with BBC political editor Laura Kuenssberg Mr Roache, the GMB union's new leader, Tim Roache, said his "biggest concern" was that Labour voters would "stay at home" on 23 June.
"I think they won't see it as the absolutely crucial vote that it is and I also think that they see it as a bunfight in the Tory party," he said.
Asked whether he thought Labour was doing enough to get its pro-Remain message across, he said it "is starting to do more".
But he argued that a bigger push was needed, warning: "The reality is that the more people that stay at home the more likely it is that we will leave the EU. I don't think we can even begin to contemplate that."
By Laura Kuenssberg, BBC political editor
Here's the strange thing. Jeremy Corbyn is campaigning to stay in the European Union. In fact nearly all of the Labour Party is.
But if you didn't know that, and you listened to his speech this morning, you would not have left the room with that overwhelming sense.
Mr Corbyn said the Labour message was "loud and clear", that the Conservative Party was a bigger threat to the country than the European Union was, and that whether on workers' rights, the environment, or renewable energy, Britain can achieve more progressive policies working with other countries in the EU than alone.
But as part of his "Remain and Reform" agenda, the Labour leader listed almost as many downsides with the EU as positives.
On Jeremy Corbyn - who has been urged to make a bolder case for staying in the UK - Mr Roache said he viewed the Labour leader as "a half-hearted Remain" but urged the party to get behind him and campaign vigorously to stay in the EU.
"I think he probably could do a bit more, let's hope he will," he said.
Speaking on BBC Radio 4's Today programme, Labour's Mary Creagh said she had been contacted by party supporters asking what its position was on the EU referendum.
Labour should treat the referendum "as though it was a general election campaign", she added.
Labour's welfare spokesman Owen Smith told the programme Mr Corbyn understood the need to make a "to make a strong Labour case" in the EU debate.
In his speech at the Institute of Engineering Technology on Thursday, Mr Corbyn - who has been a long-standing critic of the EU and who is regarded as the most Eurosceptic Labour leader in years - said British workers benefit from a host of rights and protections because of EU legislation.
He said the European social chapter and other EU directives had secured:
28 days of paid leave and a limit on working hours for more than 26 million employees
Eight million part-time workers being given equal rights with full-time colleagues
One million temporary employees have the same rights as their permanent colleagues
Guaranteed maternity leave rights that are used by 340,000 women every year
"It's important to understand the benefit of these gains," he said. "It means workers throughout Europe have decent rights at work, meaning it's harder to undercut terms and conditions across Europe."
Mr Corbyn also tackled the issue of immigration - saying government austerity policies since 2010 had been the cause of problems for communities with high immigration rather than the migrants themselves who, he said, often worked in public services such as the NHS.
But Leave campaigners, including Vote Leave's Ms Stuart, say the EU has been "a disaster" for workers, pointing out that unemployment levels across the eurozone are "in the double digits".
The Labour MP has also dismissed Remain's argument that workers' rights have been secured by Europe.
"Workers' rights are not something that have been gifted to us by the EU, they have been hard won here at home and should be protected by a Parliament that is properly accountable to voters in the UK."
She has said the only way to "take back control of our economy, our democracy" is to leave the EU.