Five security checkpoints have been attacked in higher Sinai, along the Egypt-Israel border, days after 16 border guards were shot dead in an attack in the peninsula.
One person was injured in the attacks late on Tuesday night, sources told Al Jazeera.
A cement production company in Sinai, which belongs to the military, was also attacked.
Two gunmen suspected in that attack have reportedly been arrested.
Egyptian state media said that armed men opened fire on a checkpoint in Al-Arish city in the Sinai peninsula.
"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]," the MENA state news agency said in a report also carried on Egyptian state television.
Exchanges of gunfire continued late into Tuesday night, MENA said.
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.
Lawlessness in the rugged desert region, highlighted by the recent attacks, has spread since the fall of autocrat Hosni Mubarak in an uprising 18 months ago.
In reaction to Sunday's attacks, Egypt began to seal off smuggling tunnels into the Gaza Strip, according to security sources.
Meanwhile, in Cairo on Tuesday, crowds of angry mourners wept at the military funeral of the 16 slain guards who were killed on Sunday by attackers in Bedouin attire in the Rafah border town in the Sinai peninsula.
Days of mourning
Egypt's President Mohamed Morsi did not attended the funeral, but Field Marshal Hussein Tantawi - the defence minister and head of the Supreme Council of the Armed Forces - was present along with senior government officials and generals.
The funeral began at an army mosque in the eastern Cairo area of Nasr City where the bodies of the dead soldiers were draped in the national flag.
Thousands of Egyptians were at the ceremony, which was broadcast live on state television. Some of the mourners shouted slogans against Morsi and his Muslim Brotherhood for their links to the Palestinian movement Hamas.
"Every Egyptian feels this attack was directed against them. They all want vengeance, and there must be blood for blood," a presenter said during the broadcast.
Morsi announced on Monday three days of national mourning for the slain soldiers. For its part, Egypt's military pledged to hunt down those behind the killing.
It described the attackers as "enemies of the nation" who must be dealt with by force and suggested they were Sinai-based Egyptian fighters who received Palestinian support from the Gaza Strip.
No group has yet claimed responsibility for the Sinai attack.
Egypt and Israel say both Islamist fighters from the Sinai and Palestinian allies from the Gaza Strip are active in northern Sinai, attacking both Egyptian security forces and staging raids across the border into Israel.
An Egyptian armed forces' statement suggested that groups on both sides of the border may have been involved.
"The armed forces have been careful in the past months and during the events of the [Egyptian] revolution [in 2011] not to shed Egyptian blood ... but the group that staged yesterday's attack is considered by the armed forces as enemies of the nation who must be dealt with by force," it said.