The ordinance cleared on Saturday provides up to 10 years imprisonment for "love jihad".
Uttar Pradesh Police has filed its first case under the state's new anti-conversion law, accusing a Muslim man of putting pressure on a woman to change her religion.
The case was reported on Saturday at the Deorania Police station in Bareilly district under the Uttar Pradesh Prohibition of Unlawful Conversion of Religion Ordinance, 2020, cleared on Saturday by Governor Anandiben Patel.
The Hindu woman's father has alleged that the accused was trying to force her to convert to Islam. He has also reported that the accused, on being confronted by his family, threatened to kill them.
"The boy had abducted the girl. So another case was already filed against him. He was putting pressure on the girl to convert. A case has been now filed under Sections 3 and 5 of the new ordinance. This is besides sections of the IPC," Sansar Singh, Bareilly Rural Superintendent of Police, told media.
"The boy is on the run, we are looking to arrest him," Mr Singh said.
Chief Minister Yogi Adityanath's Cabinet, on Tuesday, okayed the ordinance, proposing a maximum punishment of 10 years for "love jihad" related offences.
The new law mandates a jail term of the accused between one to five years, with Rs 15,000 penalty, if convicted of carrying out forceful conversions for marriage.
According to the new law, a marriage will be declared "null and void" if the conversion of a woman is solely for that purpose, and those wishing to change their religion after marriage need to apply to the district magistrate.
In recent weeks, BJP-run states like Uttar Pradesh, Haryana, and Madhya Pradesh have revealed plans to enact laws to counter alleged attempts to convert Hindu women to Islam in the guise of marriage.