JERUSALEM, March 23 (Crispian Balmer/Reuters) - A bomb planted in a bag exploded near a bus stop in a Jewish district of Jerusalem on Wednesday, killing a woman and injuring at least 30 people, in an attack police blamed on Palestinian militants.

No one claimed responsibility for the blast, which coincided with an upsurge of violence on the Gaza border that has led to fears of a new war between Israel and the Islamist group Hamas, which governs the Gaza Strip, after months of relative quiet.

Medics said three people were seriously hurt by the explosion, which hit one of the main routes into central Jerusalem in the afternoon, shattering the windows of a nearby bus. The dead woman was in her 60s and died in hospital.

Police said it was a terrorist attack -- Israel's term for a Palestinian strike. It was the first time Jerusalem had been hit by such a bomb since 2004.

World leaders condemned the bombing, as well as a barrage of rockets and mortars fired from Gaza in recent days.

The United States calls on the groups responsible to end these attacks at once and we underscore that Israel, like all nations, has a right to self-defense, US President Barack Obama said in a statement released in Washington.

Palestinian leaders in the West Bank, who are opposed to Hamas, also denounced the attack.

I condemn this terrorist operation in the strongest possible terms, regardless of who was behind it, Prime Minister Salam Fayyad said in a statement.

At the height of a Palestinian uprising that began in 2000, but which died out in recent years, militants carried out dozens of often deadly bombings in Jewish neighborhoods of Jerusalem.

Internal Security Minister Yitzhak Aharonovitch said the bomb weighed about one or two kilos (2 or 4 lb). It exploded in a small suitcase on the sidewalk next to the bus stop, he told Israel's Channel 2 television.

Blood stained the pavement and many people had to be treated for shock. Israeli television broke into normal programming to show scores of ambulances converging on the scene, taking the injured to nearby hospitals.

I saw two women lying on the ground, unconscious and covered in blood, medic Motti Bukchi, who arrived swiftly on the scene, told Israel's Channel Two television.

PEACE IMPASSE

Peace talks aimed at ending the decades-old conflict between Israel and the Palestinians broke down last year after Israeli Prime Minister Benjamin Netanyahu refused to extend a partial freeze on Jewish settlement building in the West Bank.

Israeli security officials have cautioned that the absence of any peace initiative could spark a new Palestinian uprising. Over 500 Israeli civilians died in 140 Palestinian suicide bomb attacks from 2000 to 2007. More than 4,500 Palestinians were killed by Israeli forces in the same period.

US Defense Secretary Robert Gates, on a visit to Cairo, denounced what he called a horrific terrorist attack but said he did not think the situation in Israel was deteriorating.

Egyptian Foreign Minister Nabil Elaraby urged Israel to show restraint and said no one should give it an excuse to use violence -- an apparent reference to Palestinian militants.

Netanyahu delayed his departure for Russia by several hours on Wednesday to consult with security officials, but refused to cancel the trip altogether.

Earlier, the prime minister had warned Hamas over rising violence in Gaza. Hamas says its attacks this past week have been in response to recent Israeli bombings and killings.

On Tuesday, Israeli strikes in the Gaza Strip killed four Palestinian civilians, including three children playing football, and five militants, medical officials said.

Netanyahu has voiced regret for the civilian deaths but said Israel could not ignore attacks on its territory.

It could be that this matter will entail exchanges of blows, and it may take a certain period of time, but we are very determined to strike at the terrorist elements and deny them the means of attacking our citizens, he told parliament.

Israel launched a three-week war on the impoverished coastal enclave in 2009, killing about 1,400 Palestinians and drawing heavy international censure. Hamas, which seized control of Gaza in a 2007 coup, had mostly held fire since.

(Writing by Jeffrey Heller and Crispian Balmer; additional reporting by Dan Williams, Ori Lewis and Ari Rabinovitch in Jerusalem and Mohammed Assadi in Ramallah; editing by Janet Lawrence)