KABUL, May 16 (Reuters) - Thousands of Afghans protested outside the Pakistani embassy in Kabul on Wednesday, chanting "Death to Pakistan, Death to Musharraf", after the bloodiest clash in decades on the disputed border last weekend.

Pakistani forces crossed into Afghan territory and killed 13 people, including children and police, in two days of clashes, according to the Afghan Foreign Ministry.

Security was tight outside the embassy and there was no sign of violence, though protesters have stormed Pakistan's missions in Kabul several times in the past.

"We will teach you a lesson, Pakistan," shouted Hazrat Mir Zazai, joining other protesters yelling anti-Pakistan slogans on loudspeakers.

Relations between the neighbours, both U.S. allies in a war on terrorism, have deteriorated sharply in the past 18 months as an insurgency in Afghanistan gathered strength,

Both sides blame the other for a resurgence of Taliban militants.

Many of the protesters come from Paktia, the southeastern province where the clashes occurred.

The Foreign Ministry issued a strongly worded statement on Monday urging "Pakistan to prevent such action that would entail dangerous consequences for the stability of the region".

Foreign Minister Rangeen Dadfar Spanta -- who was removed from office by parliament at the weekend but is still working until a court ruling -- had sent a letter to U.N. Secretary-General Ban Ki-moon to protest "the attacks of Pakistani forces".

Pakistan said the clashes began when Afghan troops, without provocation, fired on a handful of border posts in the Kurram tribal district in northwest Pakistan.

A NATO soldier was killed and four wounded on Monday in an ambush by "unknown assailants" while returning to the Afghan side after a flag meeting with Pakistani officers to discuss how to end the skirmishes on the border, a statement by the Western military alliance said.

The latest blow to relations comes just a little over two weeks after the presidents of Pakistan and Afghanistan met in the Turkish capital Ankara. They agreed to end their disputes and intensify cooperation.

There are plans to hold a 700-strong jirga, or council, in Kabul in August, incorporating tribal leaders and elders from the ethnic Pashtun lands on both sides of the border to persuade people of the region to reject the Taliban and their allies.

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