"It is World Refugee Day and I chose to be here on this day," Ashton said in Gaza on Thursday.
"I chose to be here to underline the situation in Gaza, and to say that we support the work of (United Nation's agency for Palestinian refugees) UNRWA and want to see a future for the people of Gaza."
"We want to see the crossings open, and the economic situation improved," she said in a remark directed to Israel at a joint press conference with UNRWA Commissioner General Filippo Grandi.
Ashton praised UNRWA's work and pledged that the EU would "continue to be the strongest supporter, that we will give the financial support that is needed, but also the political support."
Hamas officials also urged Ashton to "act immediately to lift the siege of Gaza" and "remove Hamas from the list of terrorist organizations" of the EU, arguing that "the movement defends its people and believes in democracy and openness to the world."
Gaza has been blockaded since 2007, a situation that has caused a decline in the standard of living, unprecedented levels of unemployment, and unrelenting poverty.
The apartheid regime of Israel denies about 1.7 million people in Gaza their basic rights, such as freedom of movement, jobs that pay proper wages, and adequate healthcare and education.
UN Humanitarian Coordinator James W. Rawley said in April that a new round of Israeli restrictions on the Gaza Strip was impacting food supplies and would have “serious” effects if continued.