The accusations, made in a news conference explaining the military's ongoing offensive in the volatile northern Sinai area, were a rare public criticism of the Palestinian militant group by the military since the July ouster of Islamist President Mohammed Morsi in a coup.
Egyptian media has been pointing the finger at Hamas for meddling in Egypt's affairs, some suggesting that the ouster of Morsi, an ally and fellow Islamist, has prompted the group to cause trouble in Sinai by supporting militant groups there. Hamas officials have denied interfering and complain that Egyptian authorities have imposed the strictest restrictions on the border and its vital Rafah crossing in years.
"Securing borders is a joint mission for those sharing the borders. It is also up to Hamas to exert more effort to control the borders," Col. Ahmed Mohammed Ali said. "Egypt deserves more than the effort we are seeing from the other side to secure the border."
Ali said troops have arrested 309 militants and criminals, including Palestinians, in operations that began in the region in July and were stepped up with an offensive last weekend. They also uncovered weapons caches that included anti-aircraft missiles, long-range mortars, rocket-propelled grenades and tons of explosives, he added.
In the last 48 hours, he said, troops had discovered explosives laid in tunnels along the border and under Egyptian watchtowers, with detonating wires running back into Gaza.
"This will call for new measures ... to deal with these threats that endanger the forces and the borders," Ali told reporters, adding that Egyptian intelligence had also discovered that a number of insurgent attacks in Sinai had been coordinated with Gaza-based extremist groups.
Since Morsi's overthrow, militant attacks against security forces in northern Sinai have escalated, a trend Egyptian authorities blame on Morsi and his allies.
Morsi's supporters insist they are peaceful, but some have openly said the situation in Sinai will not stabilize unless he is restored to power.
In Gaza, Hamas government spokesman Ihab al-Ghussein denied militants were using the Palestinian territory as a staging ground for operations against Egypt.
"We deny any connection between Gaza, its resistance and government, and the tunnels and the explosives which were mentioned by the Egyptian army spokesman today," al-Ghussein told reporters.
Egypt's military launched the recent Sinai offensive last Saturday in response to militant attacks they say have killed more than 100 policemen and soldiers in recent months.
In the worst single attack, gunmen pulled police recruits from buses and shot 25 of them dead on Aug. 19. And last week, in a new escalation, two suicide bombers hit a military intelligence building nearly simultaneously, killing at least six troops.
During the ensuing offensive, Egyptian troops began demolishing homes along the Gaza border to block the flow of militants and weapons. Ali said houses had been knocked down on the Egyptian side up to 1 kilometer (0.06 miles) away, but that the owners would be compensated.
Meanwhile, in a case that highlights the volatility of the situation in Sinai, an Egyptian journalist who lives there was put on military trial on Sunday. Prosecutors accuse him of spreading false information about the army's counterinsurgency operations there.
Ali said freelancer Ahmed Abu-Draa, a resident of Sinai, does not have appropriate press credentials and was arrested in a restricted military zone. Abu-Draa also stands accused of lying about the army attacking mosques and relocating families in Sinai.
He said the journalist's fate will be decided by the military court, and that spreading false information as part of an "information war" is a threat to national security.
The case has caused an outcry among journalists in Egypt, and dozens protested Saturday outside the courthouse in the Suez Canal city of Ismailia. Reporters Without Borders, the press watchdog, has called for his immediate release.
Abu-Draa was detained 11 days ago after he wrote on Facebook that airstrikes ostensibly targeting militants had hit civilian areas. He also accused military officials of misinforming the public and questioned the military's statements about its operations in Sinai.
Few journalists have direct access to what is happening in Sinai because of security restrictions and concerns, forcing many to rely on statements by officials. Abu-Draa, an award-winning reporter who has done investigation stories in Sinai, works for several Egyptian and foreign newspapers and television channels.
Five journalists have been killed since Morsi was removed from office July 3 after nationwide protests against him. Reporters Without Borders says another 80 have been arbitrarily detained most from outlets that authorities accuse of being pro-Islamist or sympathetic to Morsi's Muslim Brotherhood group.