* Construction spending up, manufacturing growth picks up
* April consumer spending flat
* Intel falls on Altera buy, weighs on Nasdaq, Dow and S&P
* Indexes up: Dow 0.5 pct, S&P 0.5 pct, Nasdaq 0.5 pct (Updates to late afternoon)
By Caroline Valetkevitch
June 1 (Reuters) - U.S. stocks rose in late afternoon trading on Monday as more mixed economic data bolstered the view the Federal Reserve may raise rates later rather than sooner.
Data from ISM showed that the pace of manufacturing growth rose in May. Other reports showed construction spending surged in April, but consumer spending was unexpectedly flat.
With little evidence of a rebound, the Fed is in no position to start raising interest rates for the first time since 2006, Boston Fed President Eric Rosengren said.
Transportation stocks rebounded from recent losses. The Dow Jones transportation average, which has been close to correction territory, was up 1.4 percent.
"So far, economic data ... does not suggest the Fed is going to raise rates in the near future, and the fact that the economy contracted in Q1 even with rates near zero is not a good sign for the Fed," said Adam Sarhan, chief executive of Sarhan Capital in New York.
Eight of the 10 major S&P indexes were higher, with health, industrials and industrials among sectors with the most gains.
At 3:08 p.m., the Dow Jones industrial average rose 87.51 points, or 0.49 percent, to 18,098.19, the S&P 500 gained 10.76 points, or 0.51 percent, to 2,118.15 and the Nasdaq Composite added 25.97 points, or 0.51 percent, to 5,095.99.
Bristol-Myers shares rose 3.1 percent to $66.61 after the FDA accepted its application for a combination melanoma treatment.
Immunogen surged more than 70 percent, leading a rally in cancer drug makers' stocks after they presented positive data at a conference.
Amid mounting worries of a Greek default, Athens missed a self-imposed Sunday deadline to reach an agreement to unlock aid.
Intel fell 1.7 percent to $33.88 and was the biggest drag on the three major indexes after the company agreed to buy programmable-chip maker Altera for $16.7 billion. Altera rose 5.8 percent to $51.69.
Microsoft gave the S&P 500 its biggest boost. It was up 1.5 percent at $47.57.
Advancing issues outnumbered declining ones on the NYSE by 1,863 to 1,175, for a 1.59-to-1 ratio on the upside; on the Nasdaq, 1,526 issues rose and 1,197 fell for a 1.27-to-1 ratio favoring advancers.
The S&P 500 was posting 14 new 52-week highs and 6 new lows; the Nasdaq Composite was recording 96 new highs and 41 new lows. (Additional reporting by Tanya Agrawal; Editing by Savio D'Souza and Nick Zieminski)