Hours ahead of a scheduled visit to Israel, al-Mulki said freeing Jordanian prisoners was "a basic demand" in line with Jordan's peace treaty with Israel.
"Every prisoner occupies a paramount importance in our hearts. We cannot speak … with Sharon … without raising the issue of Jordanians jailed after border clashes," he said. "We will not forget the prisoners."
Soon after al-Mulki voiced the demand, a senior Israeli official said about 20 prisoners might be transferred to Jordanian custody.
He said Israel would seek to satisfy demands raised by the visiting foreign minister, but objected to freeing the men because they had all been convicted by Israeli courts.
Al-Mulki's visit to Israel is the first by a senior Jordanian official since 2001. Jordan renewed ties with Israel, restoring an ambassador to Tel Aviv after the 8 February peace summit in Egypt.
Jordan and Egypt are the only Arab countries to have made peace with Israel. Egypt signed a treaty in 1979. But Jordan withdrew its ambassador after the outbreak of Israeli-Palestinian violence in September 2000.
Al-Mulki spoke after discussing Middle East peace with Palestinian leaders including President Mahmud Abbas in the West Bank city of Ram Allah, before he was to visit neighbouring Israel for talks.
Al-Mulki also met Abbas
Jordanian officials say Israel is holding about 20 Jordanian prisoners, including several jailed before Jordan's peace treaty with Israel was signed in 1994.
Al-Mulki said he would suggest further steps for Israel to take "if we want the peace process to succeed."
Israel froze contacts with the Palestinians including plans for a withdrawal of soldiers from West Bank cities and a pledge to release 500 Palestinian prisoners after a bombing in Tel Aviv killed five Israelis.