Mr Olmert, who is on his first visit to Europe since being elected premier in March, told journalists after a joint press conference with Mr Blair that he could "not be more satisfied" following his talks at 10 Downing Street in London.
Mr Olmert, who spoke of "new winds" blowing in Europe, is trying to sell a plan of setting Israel's borders with or without agreement of the Palestinians while on a trip to London and Paris.
Mr Blair did not outwardly reject the proposal, which has received a cool reception from some Arab leaders. Mr Blair said everyone favoured a negotiated settlement.
But such discussions would only take place if the Palestinians recognised the Jewish state's right to exist, renounced violence and agreed to follow the international "road map" for peace, the British premier said.
The three principles are rejected by the government led by Hamas, the main Islamist movement in the Palestinian territories.
The "road map," drafted by the United States, Russia, the European Union and the United Nations, calls for establishing a viable Palestinian state living alongside Israel in peace.
"I don't want to go down any other path than a negotiated settlement but the reality is that this thing has got to be moved forward by negotiation or we are in a stalemate that Israel is necessarily and realistically going to want to unlock," Mr Blair said.
"We, the international community, have got a choice. We either put our best effort into making sure that negotiated settlement becomes a reality or we are going to face a different reality," he said.
Olmert warns of stalemate
During the press conference, Mr Olmert said "we prefer to have a negotiated deal. We will do everything possible in order to achieve that."
The Israeli premier also confirmed that he would be meeting Palestinian President Mahmud Abbas in "a few weeks".
He emphasised the importance, however, that the Palestinians met the three basic principles for negotiations to occur.
Mr Olmert warned: "One thing will not happen: a stalemate. Either we move in this direction and we make every possible effort or there will be another reality in the words of Prime Minister Blair and this reality is moving forward in order to change the present status quo in the Middle East."
He said his main goals were to separate Israel from the Palestinians, have a secure border, enjoy safety and security for all and enable the Palestinians to realise their dream of a Palestinian state.
He declined to be drawn on when he might implement unilateral measures.
Mr Olmert's so-called "realignment plan" would see Israel uproot 70,000 settlers from the West Bank while cementing its hold on housing blocs where most of the quarter of a million settlers live.
US President George W Bush has called the plan "bold" but has also told Mr Olmert that he must first exhaust all efforts to reach an agreement with Mr Abbas.
Tensions between Israel and the Palestinians were raised on Friday by the death of eight Palestinian civilians in an explosion on a beach in the northern Gaza Strip, an incident that prompted Hamas to end an 18-month truce.
Asked whether Israel could kill Hamas ministers, Mr Olmert told journalists accompanying him in London: "Whoever is implicated in terrorism cannot claim to have immunity."
Mr Olmert will also visit Paris for meetings with French President Jaques Chirac and Prime Minister Dominique de Villepin on Wednesday.