AFP correspondents heard heavy shelling throughout the morning as loyalist tanks thrust into the western suburbs of Libya's third largest city.
At least four people were killed and some 30 wounded in the fighting, medical sources said. Clashes overnight had killed another six and wounded dozens more.
"The tanks are in Al-Ghiran et Zawiyat Al-Mahjub and have been halted by our men," a rebel commander told AFP.
AFP correspondents heard one or more NATO aircraft overflying the city for more than two hours in the late morning but no air strikes were heard.
The few residents who ventured out expressed exasperation at the lack of a military response from the Western alliance to Gaddafi's armour. "NATO has to help us. What are they waiting for?" asked one resident in his 40s.
Unlike on previous days of the more than six-week-long siege, the resident declined to give his name, an indication of the mounting fear in the city that Gaddafi's forces are poised to retake it.
"We have seven intensive care beds but at the moment there are eight who need them," a medic in the city's main hospital told AFP.
"The eighth is having to make do without a respirator and the nurses are having to help him breathe manually. If we get another critically ill patient, he will die," said the doctor, a Western volunteer.
The last major rebel bastion in western Libya, Misrata is surrounded by pro-Gaddafi forces and entirely dependent on supply by sea. Loyalist troops have repeatedly pounded the port, killing two rebel fighters on Sunday alone, witnesses said.
In the capital, preparations were under way for the afternoon funerals of Gaddafi's second youngest son Seif al-Arab, and three of his grandchildren. Government spokesman Mussa Ibrahim told reporters early on Sunday that the house of Kadhafi's son "was attacked tonight with full power.
"The attack resulted in the martyrdom of brother Seif al-Arab Moamer Gaddafi, 29 years old, and three of the leader's grandchildren," Ibrahim added.
Gaddafi and his wife were in the building with his son, Ibrahim said, calling the strike "a direct operation to assassinate the leader," who he said "is in good health -- he wasn't harmed. His wife is also in good health."
The children killed were a boy and a girl, both aged two, and a baby girl of four months, he added.
Demonstrators torched vacant British and Italian diplomatic buildings in Tripoli in response, prompting Britain to expel the Libyan ambassador.
Italy boosted security checks on Sunday when Gaddafi threatened to "bring the battle to Italy" after the Rome government's decision to join the NATO-led air strikes.
But on Monday Prime Minister Silvio Berlusconi sought to play down the threats which he attributed to Gaddafi's "disappointment" in Italy, Libya's former colonial ruler.
"I would not attach much importance to this statement," Berlusconi said.
"I think that (Gaddafi's) reaction is dictated by the disappointment provoked by Italy and is linked to the friendship treaty" the two countries signed two years ago, he told journalists in Milan.
Turkey closed its embassy in Tripoli late on Sunday following the attacks on the British and Italian diplomatic missions, Foreign Minister Ahmet Davutoglu said.
"Due to the change in the security situation in Libya and the great security risk it poses... our embassy has stopped functioning temporarily and has been evacuated," Davutoglu told reporters on Monday.
The Western alliance vowed more strikes, although the operation commander stated "we do not target individuals."
"All NATO's targets are military in nature and have been clearly linked to the... regime's systematic attacks on the Libyan population and populated areas," said Lieutenant General Charles Bouchard.
He said raids would continue until threats against civilians ceased and all of Gaddafi's forces "have verifiably withdrawn to their bases, and until there is full, free and unhindered access to humanitarian aid to all those in Libya who need it."
China renewed its call for a ceasefire and urged NATO not to exceed the terms of the UN Security Council resolution which provided for military action to protect civilians.
"The Chinese side has all along opposed any actions that overstep UN Security Council authorisation, we hope that all sides can immediately cease fire and politically resolve the current crisis in Libya through dialogue," foreign ministry spokeswoman Jiang Yu said.
An international coalition began carrying out strikes on March 19 under the UN Security Council mandate. NATO took command of operations on March 31.