Egypt accused Hamas radicals of showing Islamists in Egypt how to set off car bombs and do other terrorist acts -- a charge the Palestinian Sunni group denied.
At the same time, interim Egyptian President Adly Mansour extended the nationwide state of emergency imposed 30 days ago for two more months.
Cairo's allegations against Hamas militants, aired on state TV, came a day after suicide bombers killed at least six Egyptian soldiers in two separate attacks in northern Sinai near the border crossing to Gaza, where Hamas is based.
On Tuesday Hamas rival party Fatah accused the No. 2 Hamas leader of inciting Egyptians against the country's interim government by broadcasting anti-regime, pro-Islamist disinformation on Hamas-run al-Aqsa TV.
Hamas -- an offshoot of the Muslim Brotherhood, which Egypt's military-led government is trying to crush -- denied both accusations.
Hamas deputy chief Moussa Abu Marzouk, who Fatah accused of broadcasting the pro-Islamist propaganda, said Hamas keeps out of Arab countries' internal affairs, especially Egypt's.
"Egypt's national security is Palestine's," he said in a statement quoted by the English-language Daily News Egypt.
Since the ouster of Egyptian President Mohamed Morsi July 3 and the anti-Brotherhood crackdown that followed, Hamas has been accused by Fatah of seeking to stir up Egyptian internal strife to undermine the military and its government.
Hamas has claimed since late July that Fatah, the party of Palestinian President Mahmoud Abbas, is trying to smear its rival in the hope of turning Egyptian media against it.
A Hamas political adviser told Hamas' al-Ray news agency Thursday the Palestine Liberation Organization, which Abbas also runs, was behind the alleged smear campaign to create hostility between Egypt and Hamas so the Egyptian army would launch a military offensive on the Gaza Strip, which Hamas governs.
He said the alleged campaign wouldn't work.
"The geographical and historical depth between the two countries precludes such possibility," Yousef Rizqa told the news agency.
At the same time, Mansour extended Egypt's one-month state of emergency another two months because of the country's continued strife, state-owned newspaper al-Ahram reported.
The strife includes the attempted assassination of Egypt's interior minister Sept. 5 in a bomb explosion on a busy Cairo street. The explosion instead killed at least one policeman and one civilian and injured many others.
Hard-line Islamist group Ansar Bayt al-Maqdis, based in Sinai, claimed responsibility for the assassination attempt.
The state of emergency -- imposed Aug. 14, the day police stormed two Islamist sit-ins against the country's military takeover and killed more than 600 protesters -- includes the suspension of most rights afforded criminal suspects.
A nighttime curfew is still in effect in much of the country to deter protests, the newspaper said. Train service remains shut down around the country to prevent Islamists from converging on Cairo.
"The curfew in the 14 governorates will be reviewed according to the state of security in each location," a government source told the newspaper.
"However, the curfew might shorten to midnight until 5 a.m. with the start of the school year" on Sept. 21, the source said.
The curfew currently runs from 11 p.m. to 6 a.m., except for Friday, when it starts at 7 p.m.