The state election is being seen as a referendum on his decision to ban high value banknotes in the country.
The move led to a cash shortage, hurting individuals and businesses.
"The government will be judged on the popularity or lack of popularity of its demonetisation policy in India`s most populous state," said Ashok Malik, a fellow at Delhi`s Observer Research Foundation.
Mr Malik added that the performance of Mr Modi`s governing Hindu nationalist Bharatiya Janata Party (BJP) in the state was important because it will be seen as an indicator for the country`s national politics.
The move to scrap 500 ($7.60) and 1,000 rupee notes in November was intended to crack down on corruption and so-called black money or illegal cash holdings.
However the government has admitted that the withdrawal of high value banknotes, which was met with shock in India, has had an "adverse impact" on the economy.
Mr Modi has defended the decision, which he said was made in the interests of the poor.
He has personally led the campaigning for his party with the aim of encouraging a strong showing at the polls, which would strengthen his chances of a second term in 2019.
Voting for a new state assembly in Uttar Pradesh will be staggered over several weeks, with results released on 11 March. The polls currently suggest that the BJP is tied with Akhilesh Yadav`s Samajwadi Party and Congress.
The northern state voted overwhelmingly for Mr Modi`s BJP in 2014.
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