The Republican’s 2019 spending proposal will also roll out his long-touted infrastructure plan designed to use $200m of federal funds to stimulate $1.5tn (£1.08tn) in local and private spending on roads, bridges and other projects.
But it will land in Congress just days after the President signed a $300bn budget pact to end a government shutdown, meaning it will have to be rewritten.
That agreement included $165bn in defence spending and $131bn for non-military domestic matters and, combined with Mr Trump’s flagship tax cuts, is set to increase the annual deficit.
The President’s budget plan is likely to be criticised by conservatives who fear Republicans are embracing deficit spending. During the campaign Mr Trump repeatedly insisted that Mexico would pay for his border wall, but the country refused.
Last autumn he declared the opioid crisis a “public health emergency”, urging Americans to be “the generation that ends the opioid epidemic”. He has already directed federal agencies to use all resources possible to tackle the problem and the proposed $13bn increase will go towards addiction prevention, treatment and long-term recovery.
Mr Trump’s $4tn budget proposal would take the annual budget deficit to more than $1tn, double what his last plan had predicted for 2019, according to the Committee for a Responsible Federal Budget watchdog group.
Presidential budgets are viewed largely as suggestions by Congress, which has the constitutional authority to decide spending levels.
Mick Mulvaney, head of the Trump administration’s budget office, said in a statement the proposal would recommend cuts that would lower the deficit by $3tn over 10 years.
“The budget does bend the trajectory down,” Mr Mulvaney told the Fox News Sunday programme. “It does move us back towards balance. It does get us away from trillion-dollar deficits.”
“These are spending caps,” he added. “They are not spending floors. You don’t have to spend all that.”
World news in pictures
Mr Trump’s proposal would again spare Social Security retirement benefits and Medicare as he promised during the 2016 campaign.
And while it would reprise last year’s attempt to scuttle Obamacare and cut back the Medicaid programme for the elderly, poor and disabled, his allies on Capitol Hill have signalled there is no interest in tackling hot-button health issues during an election year.
It promises 3 per cent economic growth, continuing low inflation, and low interest yields on US Treasury bills despite a large amount of new borrowing.