(Reuters) -- Armed men opened fire on a security checkpoint early Wednesday in al-Arish, Egypt, on the Sinai peninsula, state media said, three days 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 official Middle East News Agency said.

"Unknown armed men opened fire on a checkpoint on the main road between Al-Arish and Rafah," on the border between Egypt and Gaza, MENA said in a report also carried on Egyptian state television.

Lawlessness in the rugged desert region has spread since the fall of Hosni Mubarak 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.

On Tuesday, Egypt began to seal off smuggling tunnels into the Gaza Strip, a security source said.

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

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 food and fuel that are a lifeline for the small territory's population.

"The campaign aims at closing all the openings between Egypt and the Gaza Strip that are used in smuggling operations," said the security source.

Security forces on Tuesday stormed the homes of several Egyptians in al-Arish who were suspected to have ties with jihadi groups, and detained them pending investigations, according to security sources in Sinai.

Several Palestinian residents in the town who did not have official permits to enter Egypt were also taken to police stations for questioning, the sources said.

The government in Cairo said the gunmen behind Sunday's attack had reached Egypt via the Gaza smuggling tunnels.

No one has claimed responsibility. The Egyptian army said 35 militants were involved and that mortar bombs fired from Gaza landed in the area during the operation.

"Extensive meetings are currently taking place between top officials in the army, interior ministry and border guard to come up with a plan to detect and find the criminals behind Sunday's attacks," a Cairo security source said.