No date for the proposed visit was announced in Jerusalem
Israeli Prime Minister Benjamin Netanyahu has been invited to visit Egypt, Israeli officials say.
The offer was made during talks between Mr Netanyahu and Egyptian intelligence chief Omar Suleiman in Jerusalem.
Mr Suleiman also met Israeli Foreign Minister Avigdor Lieberman, who last year angered Egyptians with comments about the Middle East peace process.
Mr Suleiman also discussed efforts to release of an Israeli soldier seized by Palestinian militants in 2006.
Gilad Shalit was captured by militants, including members of the Hamas group which runs Gaza, in a raid into Israel which also left two Israeli soldiers dead.
During the Jerusalem talks, Mr Netanyahu told Mr Suleiman that "Israel and Egypt have common interests, and the most important one is peace," Israel's Haaretz newspaper reported.
In his turn, Mr Suleiman delivered an official invitation from Egyptian President Hosni Mubarak to Mr Netanyahu to visit Cairo. No date was announced.
It was their first meeting since a cabinet led by Mr Netanyahu, a right-wing politician, took office in Israel.
Mr Suleiman also held separate talks with Mr Lieberman.
The Israeli foreign ministry later said in a statement that Mr Lieberman "expressed his respect and appreciation for Egypt's leading role in the region and his personal respect for Egyptian President Hosni Mubarak and Minister Suleiman".
Mr Lieberman, who heads the ultra-nationalist Yisrael Beitenu party, last year caused outrage in Egypt by saying Mr Mubarak could "go to hell" for refusing to make an official visit to Israel.
Mr Suleiman has led Egyptian efforts to mediate a lasting ceasefire between Israel and Palestinian faction Hamas, which controls the Gaza Strip.