"Please note that whenever, wherever if there has been any mistake and shortcoming on our part, I assure you that we will apologise to you by bowing our heads," he said while addressing a gathering of Muslims here. (Agencies)
He did not make specific mention to any "mistake" but was apparently referring to Gujarat riots in which Modi is tainted.
Singh, who talked about the Gujarat riots and allegations against Narendra Modi during his address, insisted that BJP was not against Muslims and the community should not fall prey to the propaganda against the party and the Gujarat Chief Minister.
Asking muslims to vote for BJP this time for the sake of the nation, he said the community should help it form a government which would make India strong and ensure respect for humanity without allowing any kind of hatred.
"Try us once. If we don't come up to your expectations, don't look at us ever again," he said at the event "Modi for PM - Mission 272+ - role of Muslims" here.
"Unko dekha baar baar, kamse kam humko dekho ek baar (You have seen them so many times, atleast try us once)," he said.
Talking about the 2002 Gujarat riots, Rajnath Singh said Congress engineered such a propaganda as if Modi had ordered the massacre of all muslims at that time and is now not even ready to accept the clean chit given to him by the courts.
"Congress is playing vote bank politics to defame Modi and BJP... Try and understand this, they want muslims to move away from BJP," he said.
"Now, the court has also given him a clean chit, what else is left against him," the BJP chief said.
His colleague Arun Jaitley also sought to woo the muslims, saying BJP does not treat minorities as "instruments of political power" but treated them as equals.
"An organised campaign has gone on for several years to create a fear factor amongst the minorities about the BJP," he said, adding the party has "no prejudice" against them and appealed them to shun vote bank politics.
He said muslims should support BJP to help make India a "riot-free country where all citizens including minorities are guaranteed security and treated as co-equals with no discrimination".
The BJP chief said the Indian Constitution does not provide for reservation on religious lines. "Anyone who is poor should be given reservation, be it Muslims, Christians ..., and not on religious basis. Why divide people on the basis of religion. There should be equality."
The party plans to convene at least one thousand such conferences to woo the muslims and allay their "misconceptions".
"Please note that whenever, wherever if there has been any mistake and shortcoming on our part, I assure you that we will apologise to you by bowing our heads," he said while addressing a gathering of Muslims here.