U.S. equities capped their strongest three month gain in a decade over the first quarter, while the economy continues to expand and the jobless rate sits at the lowest level in a generation, but President Donald Trump and his team think the Federal Reserve should move quickly to cut interest rates in order to ensure the current boom remains on track.

Trump Tweeted late Friday that the Fed's "mistaken" December rate hike, as well as its "ridiculously timed quantitative tightening" capped gains for both U.S. and global equities and blunted the growth potential of the domestic economy.  Larry Kudlow, who leads the White House's National Economic Council, echoed that sentiment, telling CNBC Friday that while the U.S. economy is doing well, the Fed should still look to cut rates by a further 50 basis points -- from its current range of 2.25% to 2.5% -- if not immediately, at least "at some point".

Investors have, for the most part, discounted the President's suggestion, with the CME Group's FedWatch tool suggesting around a 40% chance of on Fed rate cut between now and the end of the year, a figure that roughly matches bets place prior to the President's late Friday Tweets.

The U.S. dollar was also holding onto its modest year-to-gain of 0.98% in early Monday trading although much of the recent moves on the dollar index, which tracks the greenback against a basket of global currencies, is linked to weakness in the euro.

The European single currency eased to 1.1230 against the U.S. dollar after a weaker-than-expected estimate of March inflation for the Eurozone, which came in at 1.4%, suggested the European Central Bank may have to take an even lighter stance on forward rate guidance in the months ahead.

U.S. economic data, as well, is holding firm, with the Atlanta Fed's GDPNow tracker, a real-time benchmark for domestic growth, improving to a first quarter reading of 1.7% last week from a prior forecast of 1.5%

"The current US economic position looks fairly decent. The strong jobs market is resulting in rising worker pay and means consumer confidence is back close to cycle highs", said ING's James Knightley. "There have also been better retail sales and durable goods orders numbers of late while the ISM reports continue to point to healthy growth rates. Meanwhile, a 60 basis point plunge in the interest rate on a 30-year fixed rate mortgage offers support to the real estate market."

"If progress can be made on US-China and US-EU trade talks that can lift some of the gloom surrounding the global economy, we may see markets gradually re-appraise the growth outlook and prospects for inflation," he added.

China's factory output, in fact, rose the most in eight months in March, topping the 50 point mark that separates growth from contraction for the first time since November, suggesting not only that $300 billion in fresh stimulus from Beijing in starting to help the world's second-largest economy but also that near-term hopes of a trade deal with the United States are starting to impact investment.

Pantheon Macroeconomic's Ian Shepherdson argues the Fed won't want to risk its hard-won price stability and also thinks the Fed's ability to cut rates will likely be thwarted by both a trade deal with China and rising U.S. wages -- which he thinks may accelerate at a 4% clip later this year -- that could boost domestic inflation as the economy remains on solid footing.

Friday's March non-farm payroll report, which is expected to show that employers added a net 175,000 new jobs while average hourly wages rose 3.4% from last year, will go some way towards influencing the Fed's thoughts on inflation, particularly if hints of a near-term China trade deal come form this week's visit from China's Vice Premier Liu He.

"The Fed wants price stability-currently defined as 2% inflation-and maximum sustainable employment," Shepherdson wrote in a recent client note. "Right now, Fed officials are keen to point out now that the twin objectives are being met"

"Policymakers' next battle, then, is to hold onto what they have engineered," he added.