Justice Vikram Nath passed the order after arguments from petitioner Ajay Rai as well as the respondent concluded.
The court also granted time to both parties till December 1 for filing any further written submissions.
Rai, who is a sitting Congress MLA from Pindra assembly segment of Uttar Pradesh, was the party's candidate from Varanasi in the 2014 general elections.
He has challenged the election of Modi on a number of grounds including alleged discrepancies in his nomination papers, expenditure on election campaign and use of religious sentiments for garnering votes.
The team of lawyers arguing on behalf of Rai was led by senior high court advocate Umesh Narain Sharma, who is a former head of the legal cell of the Congress party's state unit.