BAGHDAD — A majority of the foreign troops that have been part of the multinational coalition in Iraq will depart in the next few weeks or have already done so, because they will no longer have the authority to operate in Iraq when the United Nations resolution authorizing their presence expires Dec. 31.

The Tongans ended their deployment on Friday, the Azerbaijanis a few days ago, the Poles last month and the Macedonians and Bosnians in the past few weeks. South Korean and Georgian troops have also left, the latter somewhat earlier than planned when fighting broke out in their country in August. In many cases these contingents have included fewer than 200 soldiers, although some, like the troops from Poland, were as large as 900.

That will leave in Iraq only British soldiers and a very small number from two or three other countries, along with the American military. Because the British will remain after the end of the year, the Iraqi and British governments are negotiating a security agreement.

There are 4,100 British soldiers in Iraq, the vast majority of them in Basra.

The agreement being sought with Britain, like the pact with the United States that was approved by Iraq’s Presidency Council on Thursday, would go into effect when the United Nations resolution expires at the end of the month. The resolution authorized and governed the presence of international forces in Iraq. It is not clear whether the British will pursue a formal agreement, which would require parliamentary approval, or put in place a less formal pact that would not need parliamentary approval.

“The two sides started negotiations a month ago to reach an understanding between the two sides on the withdrawal of British troops from Iraq,” Labid Abawi, the Iraqi under secretary of foreign affairs, said in an interview with the semi-official government Web site Aswat-al-Iraq.

A diplomat at the British Embassy in Baghdad, who spoke on condition of anonymity because he was not authorized to speak to the news media, said that the negotiations were continuing, but that the mission of British forces would be significantly reduced by early next year. By then, the British military will be involved almost exclusively in training Iraqi troops, according to Iraqi officials.

“There’s an end-of-year deadline, but we hope to be able to make an announcement soon,” the British diplomat said. “We expect that our forces will complete most of their tasks in Iraq in the early months of 2009, and following that there will be a fundamental change in the nature of our mission in Iraq.”

In contrast to the charged debate over approving the security agreement with the United States, lawmakers appeared to think that if a similar agreement was reached with Britain, it would readily win approval in Parliament. Because of the small number of British soldiers that will remain in the country, a formal agreement might not even be necessary.

“There won’t be more than 500 British soldiers in Iraq after Jan. 1, 2009,” said Abbas al-Bayati, a member of Parliament’s security committee. “With such low numbers, we won’t need more than a temporary protocol between the British and Iraqi Ministries of Defense to authorize their presence.”

The Iraqi foreign minister, Hoshyar Zebari, met with Simon McDonald, the British prime minister’s foreign policy adviser, on Monday and the talks are continuing, according to the statement on the semi-official Web site.

In an unrelated development, representatives from international energy companies, including Gazprom Neft of Russia and ConocoPhillips of the United States, met Friday with members of the Iraqi Ministry of Oil at the first Iraq Energy Exposition and Conference, which was held at a nearly completed conference center at the Baghdad airport.

Many of the energy companies are in the process of bidding on oil contracts, and the executives spoke of their hopes for working with Iraq. Some executives, though, acknowledged that negotiating with the Iraqi government could be frustrating.