Ashton is the most senior diplomat to visit Gaza since Israel announced earlier this month that it would relax its three-year blockade to allow most consumer goods into the coastal strip of 1.5 million Palestinians.
Israel continues to ban virtually all exports and restricts the import of badly needed construction supplies and raw materials for industry. And along with Egypt, it prevents most Gazans from travelling.
Ashton, who was due to meet Binyamin Netanyahu, the Israeli prime minister, later on Sunday, said she would take her argument to the Israeli government "as well as of course making sure that we're putting the right kind of pressure to the international community".
Growing chorus
Other voices in the international community have also risen lately to call for the end of Israel's Gaza restrictions.
A coalition of 18 European aid and human-rights groups, including Amnesty International UK, issued a statementon Sunday saying the EU "must insist on the full lifting of the blockade of Gaza, not just its easing".
The foreign ministers of 10 southeast Asian countries have also called for unimpeded aid access to Gaza and "strongly condemned" the May 31 Israeli military raid on an aid flotilla bound for the territory, according to a draft document obtained by the Agence France-Presse (AFP) news agency.
Nine activists died in the raid, which sparked an international outcry.
The AFP obtained the document ahead of the annual meeting of the Association of Southeast Asian Nations (Asean), which begins in Vietnam on Monday.
"We reiterated the call for the unimpeded access of humanitarian assistance to the Palestinian people in Gaza in order to help alleviate their plight," the document said.
In their draft, the ministers call for a resumption of negotiations for "a final, just and comprehensive settlement with the realisation of two states, Israel and Palestine".
Along with Indonesia, the most populous Muslim nation in the world, Asean includes Muslim-majority nations Malaysia and Brunei.
Israeli disagreement
Some members of Netanyahu's administration used Ashton's visit to fire back at Israel's critics.
"(Israel) did everything it could as far as the humanitarian aid to the civilian population of Gaza is concerned," Yudi Edelstein, minister of public affairs and the diaspora, said.
Yuval Shteinitz, the minister of finance, said that "some Europeans tend to ignore the real character of the Hamas regime in Gaza. This is the most brutal regime, the Hamas regime in Gaza, on the face of earth. In Gaza, there are more executions per capita than in any other country in the world."
Ashton was not scheduled to meet with any Hamas representatives during her three-day tour of Gaza.
On Friday, she held a joint news conference with Palestinian Prime Minister Salam Fayyad.
"What we all are looking for is to end the suffering of our people in Gaza by lifting the siege and, once again, by having a policy of openness that is clearly defined and one that is implemented in the way that it is announced. What we do not want to see is actually old policy with a new name," Fayyad said.