Deputy Prime Minister Lal Krishna Advani met with members of Rashtriya Swayangsevak Sangh (RSS) on Sunday.
Their renewed demand follows an archaeological report that said a 10th-century temple with Hindu carvings existed under the rubble of the Babri mosque – which was razed by Hindu zealots in 1992 sparking nationwide riots.
The finding by the Archaeological Survey of India (ASI) has bolstered the claims of radical Hindus that the 16th century mosque was built after Muslim rulers destroyed a temple to the Hindu warrior god Ram.
"It is quite natural that there is a sense of expectancy across the country that the temple issue should move forward after the ASI report pointed to all evidence of a temple," RSS spokesman Ram Madhavhe said.
He added that the RSS brass had urged Advani, who has close ties to the Hindu right, to take a fresh look into the issue to pave the way for temple construction.
The dispute over the religious site is in the hands of the courts, which had ordered the excavations by the ASI. Muslim groups have vowed to challenge the archaeological study.
The ASI's conclusions came just weeks after a preliminary study by the same group reported no evidence of a temple at the site.
Advani's Hindu nationalist BJP party has in the past campaigned with the temple construction movement as one of its main planks.
Political analysts say that the archaeological report could give the BJP fresh ammunition for upcoming polls in five Indian states and general elections next year.