Egypt sent police reinforcements to the Sinai after an attack on a police camp on Monday in the wake of the kidnapping of security personnel, officials said.
In Cairo, the presidency said all options were on the table to secure the release of the three policemen and four soldiers held last week in the lawless peninsula.
Eighty Central Security (riot police) units and 26 armoured personnel carriers were deployed in north Sinai hours after a police camp came under fire with heavy weapons at dawn, security officials said.
Hours later, unidentified gunmen opened fire at the Oja border crossing with Israel close to another police camp with no reports of casualties, the official MENA news agency reported quoting security officials.
The attacks further heightened tensions in the peninsula after last week's kidnapping.
"The presidency did not negotiate with criminals," spokesman Omar Amer told reporters, implying that future talks were not ruled out altogether.
"There are many alternatives on the table, but the goal is the release of those kidnapped," Amer said.
"We don't want a single drop of blood spilt," he said.
On Sunday, President Mohamed Morsi ruled out negotiating with the kidnappers of three policemen and four soldiers who appeared to plead for their release in an online video, although the security official said no order had been received to launch a rescue operation.
The abductions last Thursday in the Sinai prompted angry police to shut down border crossings with Gaza and Israel.
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A video posted on YouTube earlier on Sunday appeared to show the seven hostages, blindfolded and with their hands on their heads, identifying themselves.
One of them is prodded by what appears to be a rifle held by an abductor offscreen before another hostage says the kidnappers want the release of detained Bedouin "political activists".
"What happened with the video yesterday is disgraceful. We condemn it and we will respond decisively," Amer told reporters.
The video was later removed from YouTube, which posted a message saying it violated its "policy on violence".
The policemen, who worked at border crossings, and soldiers were kidnapped at gunpoint while travelling to their homes on leave.
Earlier on Monday, assailants opened fire "for 25 minutes using heavy weapons" against El-Ahrash camp in the north of the Sinai Peninsula, without reporting casualties.
"Personnel in charge of camp security managed to repel the attack and forced the armed men to flee," he said, adding that a hunt was underway.
Several police stations in Sinai have gone on strike to protest against the abduction and in solidarity with colleagues who have closed the Rafah border with Gaza and the Oja crossing with Israel, MENA said.
Attacks on police and soldiers in the sparsely populated peninsula have surged since an uprising that overthrow president Hosni Mubarak in 2011, as have cross-border attacks on Israel.
In August 2012, suspected Islamist gunmen killed 16 Egyptian soldiers near Israel's border and commandeered an armoured vehicle into Israel, where they were stopped by a helicopter strike.