* March U.S. jobs growth lowest since last May
* U.S. fires missiles at Syrian air base
* Stocks pull back after remarks by Fed's Dudley
* All three major indexes virtually flat (Updates to late afternoon)
By Sinead Carew
NEW YORK, April 7 (Reuters) - Wall Street's three major indexes were virtually unchanged on Friday but fell well below session highs in late-afternoon trading after a key Federal Reserve official shed more light on the Fed's plan to reduce its balance sheet while investors digested a weak jobs report.
New York Fed President William Dudley discussed the U.S. central bank's developing plan for when to stop topping up bonds that expire, as it currently does, how it plans to execute it and how far it will ultimately go in shrinking its balance sheet.
U.S. Treasury yields rose after Dudley's remarks, which helped push equities lower, according to Paul Zemsky, chief investment officer, Multi-Asset Strategies and Solutions at Voya Investment Management in New York.
At 3:35 P.M. EDT (1935 GMT), the Dow Jones Industrial Average was up 3.99 points, or 0.02 percent, to 20,666.94, the S&P 500 had lost 0.59 point, or 0.03 percent, to 2,356.9 and the Nasdaq Composite had added 0.33 point, or 0.01 percent, to 5,879.28.
Also in the late afternoon, media reports emerged that Syrian warplanes had carried out strikes. Reuters cited the Syrian observatory for human rights for its report.
The news followed a pre-dawn U.S. strike in Syria. The United States fired missiles at an airfield from which it said a deadly poison gas attack was launched this week.
The news of the U.S.-Syria attack sent global stocks lower when it was announced, with the S&P 500 futures index falling as much as 0.5 percent. But most of the losses ebbed after U.S. officials described the attack as a one-off that would not lead to wider escalation.
"We have a full plate of issues today. Outside of the economy, you have China, you have Syria," said Sean Lynch, co-head of global equity strategy at Wells Fargo Investment Institute in Omaha, Nebraska.
The market had rallied after the Nov. 8 election on hopes that U.S. President Donald Trump would live up to his campaign promises for pro-business policies such as tax and regulation reform. But investors increasingly question whether they would materialize.
In the coming days it "will be interesting to watch to see if (Syria) does grab more attention from the White House and delay some of these other issues and programs they are trying to get passed through here," said Lynch.
U.S. employers added about 98,000 jobs in March, the fewest since last May and well below economists' expectation of 180,000, as bad weather hit hiring at construction sites. However, wage growth ticked up slightly and the unemployment rate fell.
Declining issues outnumbered advancing ones on the NYSE by a 1.11-to-1 ratio; on Nasdaq, a 1.09-to-1 ratio favored decliners.
The S&P 500 posted 11 new 52-week highs and two new lows; the Nasdaq Composite recorded 48 new highs and 38 new lows. (Additional reporting by Rodrigo Campos, Chuck Mikolajczak and Herbert Lash in New York, Yashaswini Swamynathan in Bengaluru; Editing by Saumyadeb Chakrabarty and James Dalgleish)