CAIRO, Aug 8 (Reuters) - Armed men opened fire on a security checkpoint on Wednesday in Egypt's Al-Arish city in the Sinai peninsula, state media said, after 16 border guards were shot dead in an attack on Sunday blamed partly on Palestinian militants.

Exchanges of gunfire continued late into the night, but there were no immediate reports of injuries, Egypt's MENA state news agency said.

Unknown armed men opened fire on a checkpoint on the main road between Al-Arish and Rafah (a city located at the border between Egypt and Israel), MENA said in a report also carried on Egyptian state television.

Lawlessness in the rugged desert region has spread since the fall of autocrat Hosni Mubarak in an uprising 18 months ago and the election of an Islamist successor whose commitment to security co-operation with Israel has yet to be tested.

Wednesday's attack on the checkpoint was the 29th since the uprising, according to MENA, which also reported that security forces had closed the road where the assault took place.

Egypt's Al-Ahram Online news website reported that clashes erupted at three checkpoints in Al-Arish on Wednesday between armed men and security forces and that one resident was injured while watching one of the clashes from the balcony of his home.

Crowds of angry mourners wept at the military funeral of the slain guards in Cairo on Tuesday after the deadliest assault along Egypt's tense Sinai Peninsula border with Israel and Gaza in decades.

In reaction to Sunday's attacks, Egypt began to seal off smuggling tunnels into the Gaza Strip, according to a security source.

A Reuters reporter in the border town of Rafah said heavy equipment was brought to the Egyptian side of the tunnels, which are used to smuggle people to and from Gaza as well as scarce food and fuel for the small territory's population.