CAIRO, May 27 (Reuters) - Egypt and the United States said they would work together to reinforce a ceasefire between Israel and Palestinian militants as U.S. Secretary of State Antony Blinken visited Cairo and Amman on Wednesday on a regional tour.

Egypt has longstanding relations with both sides in the conflict and played a key role in brokering the ceasefire after 11 days of violence, in coordination with the United States.

"We've had in Egypt a real and effective partner in dealing with the violence, bringing it to a close, relatively quickly," Blinken said in Cairo aftermeeting with President Abdel Fattah al-Sisi, Foreign Minister Sameh Shoukry and intelligence chief Abbas Kamel.

The United States and Egypt were now "working closely together build something positive", he said. Egypt, Blinken said, is vital to shared aspirations for Palestinians and Israelis to "live in safety and security to enjoy equal measures of freedom, opportunity and dignity".

Egyptian mediation in the conflict has raised questions whether Cairo might now feel under less U.S. pressure over its crackdown on political dissent that has steadily intensified in recent years.

Asked about the matter at a press conference later in the Jordanian capital Amman, Blinken said he had a "lengthy discussion" with Sisi on Cairo's human rights record and the issue of detained American citizens.

"I think the fact that we had a lengthy exchange on that with President Sisi is a reflection of the fact that it remains very much on the agenda with Egypt," Blinken said.

Sisi, who ousted the Muslim Brotherhood from power in 2013, has said there are no political prisoners in Egypt and that stability and security are paramount.

Blinken said he also discussed with Sisi Egypt's water needs and the importance of finding a diplomatic solution to the giant Grand Ethiopian Renaissance Dam. Egypt regards the dam as a potentially existential threat as the largely arid country relies on the Nile for as much as 90% of its fresh water.

Blinken arrived in Egypt after stops in Jerusalem and Ramallah on Tuesday, when he pledged that the United States would provide new aid to help rebuild the Gaza Strip, including $5.5 million in disaster relief and nearly $33 million for the U.N. Palestinian aid agency there, after hundreds of devastating Israeli air strikes.