Fighter jets, helicopters and artillery have pounded rebel positions ahead of a feared full-scale assault within days.
Tanks are trying to push into two key rebel-held areas, the opposition says.
In Damascus, another vital battleground in the war, army sources said rebels had been pushed from a last stronghold. The rebels said they had withdrawn.
Meanwhile, Iran is seeking the release of 48 Iranians kidnapped on Saturday.
Iranian diplomats and Syrian state television blamed the abduction, which took place near the shrine of Sayyida Zainab in a suburb of Damascus, on “armed groups”.
Iran has now asked Turkey and Qatar, both of whom have good relations with the Syrian opposition, to help win the release of the Iranians who it says are pilgrims.
Rebels claimed on Sunday that some of those taken were members of Iran’s elite Revolutionary Guards, according to al-Arabiya television.
Separately, Syria’s first astronaut is reported to have joined the opposition and fled to Turkey, the latest in a series of high-profile defections.
Muhammed Faris met Free Syrian Army (FSA) commanders in Aleppo and gave them his support before crossing the border, the Turkish news agency Anatolia reported.
Meanwhile, a British photojournalist who was kidnapped and wounded by Islamist militants in northern Syria has said up to 15 of his captors were from the UK.
John Cantlie and Dutch photographer Jeroen Oerlemans were held at a camp for a week in July.
The Syrian military has been steadily building up its forces around Aleppo, massing large numbers of tanks and other armoured vehicles as well as troops, in preparation for a much more intense attack.
There is already fierce fighting in and around the city as troops try to push rebel forces out from southern and eastern districts.
The army is using tanks to try to break its way into the districts of Salah al-Din and Saif al-Dawla, which lie on the main road into the city, opposition sources say.
Areas where rebels are entrenched have been bombarded by government forces and clashes have been reported in several areas, including in the heart of the old city.
A spokesman for the rebels said they were continuing to push into the centre, moving towards the historic castle in the old city. Opposition sources said there was now fighting around the castle itself – but this has not been confirmed by independent sources.
The rebels, who have also increased their numbers, are well dug in and continue to try to extend the territory under their control, our correspondent says.
The biggest advantage for the government is the use of helicopters and fighter jets; but more troops will also have to fight their way into the city if they are to stand any chance of retaking it, and that will make it a much more even battle, he adds.
Abdel Jabar Oqaida, a commander of the Free Syrian Army in Aleppo, told the AFP news agency that the restive Salah al-Din district had “come under the heaviest bombardment since the battle began” on 20 July.
A senior government security official told the agency: “The battle for Aleppo has not yet begun, and what is happening now is just the appetizer… the main course will come later.”
The fight for the key strategic city has been intensifying over the last few days, with Syrian state television reporting that troops had inflicted huge losses on what it called “terrorist mercenaries” in Salah al-Din and in other nearby areas.
In the capital, government forces claimed to have pushed out rebel fighters from their final stronghold in the city, the southern neighborhood of Tadamon. Free Syrian Army forces withdrew, an opposition activist told AFP from Beirut.
State media has reported that the whole of Damascus is now in government hands, almost three weeks after opposition forces launched a series of attacks there. Such reports are impossible to verify and the situation on the ground is changing fast.
Activists say more than 20,000 people – mostly civilians – have died in 17 months of unrest.
Meanwhile, US Secretary of State Hillary Clinton will travel to Turkey on 11 August for talks on the conflict in Syria, the US State Department said.
Hillary Clinton is adding the stop in Turkey to her lengthy tour of Africa.
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