(Recasts, updates yields; adds analyst comments, Yellen remarks) By Karen Pierog May 4 (Reuters) - A safe-haven bid helped push U.S. Treasury yields lower on Tuesday, while U.S. Treasury Secretary Janet Yellen warned that rates may need to rise to keep the economy from running too hot. The benchmark 10-year yield was last down 1 basis points at 1.5959%, holding below a 14-month high of 1.776% reached on March 30. Yields slid amid a stock selloff with the Nasdaq down more than 2%. Later in the session, longer-dated yields ticked higher after the release of remarks by Yellen, who said interest rates may need "to rise somewhat" to prevent the economy from overheating. George Goncalves, head of U.S. Macro Strategy at MUFG in New York, said while the drop in equities was probably a catalyst for Tuesday"s lower yields, there was also some skepticism creeping into the bond market. "I think there"s a mood starting to form that perhaps economic data will not be as robust as many were anticipating," Goncalves said. Data on Monday that showed U.S. manufacturing activity growth slowed in April amid supply chain challenges and increased demand sent yields tumbling. Goncalves said the upcoming April employment report could shake up the current "holding pattern" in the Treasury market. "To get this market back on track to higher yields, it needs to be a blockbuster (non-farm payrolls) number on Friday," Goncalves said. Meanwhile, the market was bracing for more supply. The U.S. Treasury said on Monday it plans to borrow $463 billion in the second quarter, assuming an end-of-June cash balance of $800 billion, as spending increases in response to the pandemic. That was much bigger than its February estimate of $95 billion, which preceded the March enactment of the $1.9 trillion American Rescue Plan. On Wednesday, second-quarter refunding details, including anticipated auction sizes for each maturity of notes and bonds, will be announced. "There"s a chance that there"s a resumption of those concerns around heavy supply and the market"s ability to digest that," said Bill Merz, chief fixed income strategist at U.S. Bank Wealth Management. The two-year Treasury yield, which typically moves in step with interest rate expectations, was last less than a basis point higher at 0.1624%. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last less than a basis point flatter at 143 basis points. The yield on 10-year Treasury Inflation-Protected Securities fell to its lowest level since February at -0.868%. It was last at -0.828%. The effective fed funds rate rose to 0.06% as of Monday, after falling to 0.05% on April 30, its lowest level since June 2020. The overnight repo rate, which measures short-term borrowing costs, fell to 0.02% on Tuesday from 0.03% on Monday. May 4 Tuesday 3:44PM New York / 1944 GMT Price Current Net Yield % Change (bps) Three-month bills 0.02 0.0203 0.002 Six-month bills 0.04 0.0406 0.003 Two-year note 99-237/256 0.1624 0.002 Three-year note 100-40/256 0.3216 0.000 Five-year note 99-166/256 0.8221 -0.008 Seven-year note 99-212/256 1.2758 -0.012 10-year note 95-192/256 1.5959 -0.010 20-year bond 95-132/256 2.1545 -0.016 30-year bond 91-140/256 2.2668 -0.022 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 11.25 -0.25 spread U.S. 3-year dollar swap 14.00 0.00 spread U.S. 5-year dollar swap 9.50 0.00 spread U.S. 10-year dollar swap -1.00 -0.50 spread U.S. 30-year dollar swap -26.50 -0.50 spread (By Karen Pierog; Editing by Nick Macfie and Will Dunham) Our Standards: The Thomson Reuters Trust Principles.