Rebel military leader Igor Strelkov was quoted as saying his forces had beaten off columns of government armour attacking from the south and west.
Pro-Ukrainian sources in the city of 425,000 people reported skirmishes.
At least 15 civilians were killed in Luhansk and the neighbouring Donetsk region on Sunday, reports say.
Germany and Russia have urged direct talks between Kiev and the rebels.
Meeting briefly in Rio de Janeiro before the World Cup final, German Chancellor Angela Merkel and Russian President Vladimir Putin called for the talks to be held by video link, Mrs Merkel's office said in a statement (in German).
The two leaders agreed that the situation in Ukraine was "tending towards a deterioration", a Kremlin spokesman said.
Pro-Russian separatist rebels have been fighting the government in Kiev since declaring independence in Luhansk and the neighbouring region of Donetsk in April.
Talks in Rio between Mr Putin and Ukrainian President Petro Poroshenko were cancelled after the Ukrainian leader announced he would not be attending the final after all.
'Seventy tanks'
A Ukrainian presidential source told Ukrayinska Pravda newspaper that an armoured unit was trying to relieve troops who had been blockaded for weeks at Luhansk airport.
Strelkov (the nom-de-guerre of Igor Girkin) said the rebels had beaten off two government armoured columns numbering between 40 and 70 tanks.
The rebels had fought artillery skirmishes with the Ukrainian army "along the front", he said.
According to a report (in Russian) on the local anti-rebel news website Informator, Ukrainian forces entered the village of Sabivka, just west of Luhansk, on Sunday. Shooting broke out and local residents took shelter in cellars, it said.
Another local pro-Ukrainian news website, 0642.ua, also reported fighting in Sabivka, quoting an unnamed local woman.
Fighting was also reported around 17:00 (14:00 GMT) just south of Luhansk, in the villages of Heorhiivka and Rozkishne, by the Luhansk news website sxid.info.
An Luhansk anonymous blogger, who tweets as @journal1st_88, wrote of hearing explosions, sirens, shooting and planes flying overhead in Luhansk.
Nine civilians were killed on Sunday in a suburb of Donetsk and six in various incidents in Luhansk, reports say.
Russian warning
The government began an "anti-terrorist operation" in April to crush the rebellion in the eastern regions.
On Friday, it suffered one of its heaviest losses when an armoured column was hit by rebel rockets in Donetsk region and at least 19 soldiers were killed and about 100 injured.
A rocket attack on the Donetsk city suburb of Marinka on Friday night killed at least four people, with the rebels and government blaming each other.
And earlier on Sunday, Russia warned of "irreversible consequences" after a man was allegedly killed on its side of the border by a shell fired from Ukraine.
The incident reportedly happened when a shell hit the courtyard of a residential building in a small Russian border town, also called Donetsk. The Ukrainian government denied firing on Russian territory.
More than 1,000 civilians and combatants are believed to have died in the fighting since April.
BBC
