NEW DELHI (Reuters) - An Indian lawmaker allied with Prime Minister Narendra Modi's Bharatiya Janata Party said he will return to India by Friday to face allegations of rape and sexual harassment made against him.

Prajwal Revanna, 33, the grandson of former Prime Minister H.D. Deve Gowda, is a member of parliament from the Hassan constituency in the southern state of Karnataka.

He is seeking a second term from his Janata Dal (Secular) party in the ongoing national elections, but has been suspended since the allegations surfaced last month.

Revanna has been out of the country since the accusations of sexual harassment were lodged following obscene video clips circulated days before the state voted in national elections on April 26. The seven-phase vote ends on Saturday.

He broke his silence on Monday, days after his grandfather urged him to return to India and face the law.

"I apologise to my parents, grandfather, family, people of the state and all party workers... I am confident I will emerge from these false cases through the court," Revanna said in a video clip aired by ANI, in which Reuters has a minority stake.

He said he will meet the Karnataka police special investigation team probing the accusations on Friday. He faces three separate cases filed by several women, local media has reported.

Revanna's comments are his first in response to the allegations. On May 1, he said on social media that he was out of the country and needed time to return to join the investigation, adding that "truth will prevail soon".

His father and former Karnataka minister H.D. Revanna was also arrested after a local court denied him relief in a kidnapping case filed against him by the son of one of the women linked to the harassment case and who had gone missing, local media reports said.

(Reporting by Tanvi Mehta; Editing by YP Rajesh and Sharon Singleton)