The Prime Minister told negotiators to get a free trade agreement (FTA) done by Diwali, in October, as he celebrated a “massive push” during the their meeting in New Delhi on Friday.
But he indicated at a press conference that he did not try to encourage Mr Modi to go further in dropping India’s neutrality over the Russian President’s invasion of Ukraine.
Mr Johnson’s two-day trip was dogged by questions over the deepening partygate scandal, with a Tory rebellion leading to a Commons investigation being opened into his alleged lying.
But he insisted he would still be Prime Minister by the festival of lights, on October 24, which he set as a date for trade deal negotiators working with one of the world’s largest economies to “get it done”.
Mr Modi appeared more relaxed about the timeframe, instead saying he wanted “good progress… by the end of this year”, but both sides applauded progress.
However, there were acknowledgements that the four chapters agreed so far were just the foothills of around 16 more to come.
Mr Johnson conceded there would be “difficult issues” ahead, including on tariffs, particularly whisky. He was also open to accepting higher levels of migration from India to take skilled jobs in Britain.
He said an FTA would allow Delhi to lift tariffs on British machinery, and in turn UK could lift tariffs on Indian rice and textiles.
The Prime Minister committed to supporting India to build fighter jets in a bid to reduce the amount of arms the nation buys from Moscow, and also wants to wean it off Russian fuel.
But India’s foreign secretary Harsh Vardhan Shringla said Mr Johnson put no pressure on Mr Modi over his position on Russia’s invasion of Ukraine.
India has declined to be publicly critical of its former Cold War ally Russia and has abstained from voting in United Nations resolutions condemning Moscow.
Mr Johnson acknowledged India’s “historic relationship” with Russia going back to the Cold War and said “they’re not going to change that” when asked whether he applied pressure on Mr Modi.
The Prime Minister sought to downplay India’s neutrality, saying Mr Modi has asked the Russian President “what on earth he thinks he is doing” in one of “several” interventions.
Mr Johnson said India and Britain can do more together on “autocratic coercion” from others, but Mr Johnson repeatedly stressed that India is a “great democracy” when asked about widespread concerns that the country is sliding towards autocracy under Mr Modi.
No 10 acknowledged the Prime Minister did not challenge his counterpart on the issue, or on concerns such as the rising anti-Muslim rhetoric under Mr Modi’s Hindu nationalists.
Mr Johnson spoke with his counterpart for around 45 minutes in the Hyderabad House government building, devoting up to 15 minutes on Ukraine, No 10 said.
His official spokesman said Mr Modi asked Mr Johnson’s “perspective” on the Russian invasion, particularly in light of his recent visit to the capital of Kyiv.
But the spokesman said Mr Johnson was “not there to talk to another democratic country about what actions they should take” when asked about whether he challenged Mr Putin.
Talks focused more on “energy and defence”, rather than calling for Mr Modi to stop buying arms, oil and gas from Russia.
The PM had been under pressure in India to speak up for minority groups as he visited a JCB factory, owned by major Tory donor Lord Bamford.
The visit to the new plant in Gujarat came while bulldozers are being used to tear down Muslim-owned properties in communal violence that has been gripping the nation.
But despite indicating he would raise the matter, Mr Johnson’s spokesman confirmed he did not discuss it with Mr Modi.
Mr Johnson’s visit to India came as his grasp on power appeared to weaken with further Tory calls for his resignation and a humiliating U-turn on his bid to a third investigation prompted by breaches of coronavirus laws.
He used the press conference on the top floor of the towering Taj Mahal Hotel to announce the eye-catching commitments of helping supply tanks to Ukraine and to reopen the British embassy in Kyiv.
Mr Johnson denied suggestions the embassy move was designed to recover his appeal among Tory MPs, his official spokesman said: “It is not, it’s a demonstration to the people of Ukraine.”