Hamid Karzai told The Associated Press in an exclusive interview on Sunday: "If a Palestinian state is recognised, we will recognise Israel, we will have relations with Israel. We will have trade with Israel.
"Israelis are people like we are," he said.
"If I have the right to live, and have a home, and have a country, Israel has the right to live and have a country. The only question here is Palestine, because we want the Palestinians to have a home and have a country."
The president said he hoped Ariel Sharon, the Israeli prime minister, would recover from the debilitating stroke he suffered last week.
"May God give him a longer life," he said.
Israel and Afghanistan have never had formal relations.
Karzai came to power following a US-led invasion of Afghanistan after the attacks of 11 September 2001.
Forging ties with Israel would infuriate Afghanistan's neighbour Iran, which has called for Israel's destruction.
Also in the Sunday interview, Karzai invited Mullah Omar, the Taliban leader, to reconcile with the government, but said he thinks the fugitive will not come out of hiding and that suicide attacks will continue in Afghanistan for "a long time".
He also said a booming drug trade is a greater threat to Afghanistan than terrorism, endangering its very existence as a nation-state.
Omar is believed to be leading holdouts in a rebellion against Karzai's government, leaving about 1600 people dead last year - the most since 2001.
Karzai invited all Afghans, "Taliban or non-Taliban", to help rebuild the country, and said that includes Omar.
Omar is thought to be hiding near
the Afghanistan-Pakistan border
The president said: "If he wants to come, he should get in touch with us.
"We would see what he has to say, of course. But I don't think he will come. He has so much on his hands against Afghanistan. We don't even know as to where he is hiding. He has to first give us an account as to what he's done."
US officials have said they believe Omar and Osama bin Ladin are hiding in rugged mountains on the border between Afghanistan and Pakistan.
Karzai said terrorism has been "relegated to little more than a nuisance" when compared with the drug scourge the country faces.
Afghanistan is the world's biggest producer of illegal narcotics, yielding enough opium to make about 450 tonnes of heroin last year - sparking warnings the country is fast becoming a "narco-state".
Karzai said the problem has criminalised the economy, tainted the country's image, hindered the development of strong government institutions and undermined young people's lives.
Afghanistan tops the world in
production of illegal narcotics
He claimed criminal gangs, including some from Europe, threaten to kill farmers if they do not turn to cultivating poppies.
Meanwhile in the US, charges against a US army captain in the beating deaths of two prisoners in Bagram, Afghanistan, have been dropped.
Christopher Beiring, 39, had been charged with lying to investigators and being derelict in his duties.
He is the third member of the 377th Military Police Company, based in Cincinnati, Ohio, and Bloomington, Indiana, to have had charges dismissed before trial, the New York Times reported on Sunday.
Four soldiers in the unit have been acquitted, two others pleaded guilty to assault and one was convicted of assault, maiming and other charges.
The decision by the commander of the Army's Air Defence Artillery Centre at Fort Bliss, Texas, was based in part on the fact Beiring did instruct his junior and non-commissioned officers to stop the overhead chaining of detainees after two senior officers insisted that he do so.
The ruling judge noted in his dismissal that the fact that a second prisoner died while similarly shackled "only shows that someone else either did not get the word about standing restraints or, more likely, got the word and chose to disregard it".