JERUSALEM, Feb 23 (Reuters) - Prime Minister Ehud Olmert will replace Israel's lead envoy to Egyptian-brokered truce talks with Hamas after he publicly criticized the government's negotiating strategy, officials said on Monday.

Amos Gilad, an adviser to Defense Minister Ehud Barak, has shuttled to Cairo to try to consolidate the Jan. 18 ceasefire that ended a three-week Israeli assault in Hamas-ruled Gaza.

Progress has been frustrated by renewed violence and a demand by Olmert that an easing of a blockade on the Palestinian territory, sought by Hamas, be preceded by an agreement by Hamas to free a captured Israeli soldier.

Olmert's office said in a statement Gilad's suspension would not hamper efforts to secure the soldier's release.

Israeli media reported late on Monday that top Olmert advisor Shalom Turgeman and Yuval Diskin, head of the Shin Bet internal security agency, would handle talks with Egypt instead.

In a critique quoted by an Israeli newspaper last week, Gilad said the government had an inconsistent approach to the talks that risked insulting the Egyptians.

It was totally unprofessional and unseemly for a civil servant to publicly attack his boss, an official in Olmert's office said, announcing that Gilad would be replaced as envoy to the negotiations.

A Barak aide hit back, saying Olmert was hurting Israel's interests by deciding not to avail himself of Amos Gilad's abilities and experience.

The dispute showed political and personal faultlines in the caretaker coalition, where Barak's center-left Labor party is junior partner to Olmert's centrist Kadima.

Both parties appear to be heading into opposition as a result of Israel's parliamentary election on Feb. 10 and the decision last Friday by President Shimon Peres to ask right-wing Likud leader Benjamin Netanyahu to form a government.

Hamas accused Israel of poor faith and urged Egypt to respond to the reshuffle by opening its own border with Gaza.

This shows that the Zionist occupation government has no intention of reaching an agreement on the truce or of concluding a prisoner swap, said Fawzi Barhoum, a Hamas spokesman.

In his comments quoted in the newspaper Maariv, Gilad deplored Olmert's attempt to wed the talks on an expanded Gaza truce to efforts to cobble together a deal in which Gilad Shalit, a soldier abducted by Hamas-led Palestinian gunmen to Gaza in 2006, would be freed.

Hamas wants Israel to release 1,400 jailed Palestinians, including senior leaders, in exchange for Shalit. The Olmert government has baulked at some of the names on the roster.

Until now, the prime minister hasn't involved himself at all, Maariv quoted Gilad as saying in the Feb. 18 article.

Suddenly, the order of things has been changed. Suddenly, first we have to get Gilad (Shalit). I don't understand that. Where does that lead, to insult the Egyptians? To make them want to drop the whole thing? What do we stand to gain from that?

Another Israeli newspaper, Yedioth Ahronoth, said on Sunday Olmert believed Gilad had failed to keep Egypt, which also borders the Gaza Strip and plays a key role in efforts to stem Palestinian arms smuggling, to its truce commitments. (Additional reporting by Nidal al-Mughrabi in Gaza; editing by Andrew Roche)