The Dow and the S&P 500, however, were lower for the month.
Investors will scour the statement for any signs of when the Fed is likely to begin raising interest rates and the pace of any subsequent hikes.
The Fed statement is due at 2:00 p.m. ET (1800 GMT), followed by Chair Janet Yellen's news conference half an hour later, with analysts expecting her to focus on signs the economy is recovering after a bumpy start to the year.
Many investors expect the Fed to signal that US interest rates will be increased in September.
"Barring an unforeseen event, the Fed will not be keen to rock the boat," said Adam Sarhan, chief executive of Sarhan Capital in New York.
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"I think Yellen has hedged her bets very carefully and remains data-dependent and I don't see a change in that strategy at the end of the meeting."
Applications for U.S. home mortgages fell last week as interest rates rose to their highest since October 2014, an industry group said on Wednesday. Mortgage application activity, which includes both refinancing and home purchase demand, fell 5.5 percent in the week ended June 12.
U.S. stocks closed higher on Tuesday following back-to-back daily declines, with merger activity offsetting market concerns as Greece struggles to avoid a default on its debt.
Relations between Greece and its creditors have become increasingly acrimonious in recent days, leaving little hope that a meeting of EU finance ministers on Thursday will make any progress.
Athens needs funds to avoid defaulting on a 1.6 billion euro ($1.8 billion) debt repayment to the International Monetary Fund on June 30, which could drive it out of the euro zone.
Sarhan said a Greek exit will affect investors psychologically because the contagion could spread to Spain, Portugal and Italy who continue to face resistance against austerity measures.
At 9:42 a.m. ET the Dow Jones industrial average <.DJI> was up 52.81 points, or 0.29 percent, at 17,957.29; the S&P 500 <.SPX> was up 5.37 points, or 0.26 percent, at 2,101.66; and the Nasdaq Composite <.IXIC> was up 14.52 points, or 0.29 percent, at 5,070.08.
All of the 10 major S&P 500 sectors were higher, with the energy index <.SPNY> leading the advances, with a 0.83 percent rise.
Kythera Biopharmaceuticals'
Qihoo 360 Technology
FedEx
Adobe Systems
Advancing issues outnumbered decliners on the NYSE by 1,828 to 864. On the Nasdaq, 1,539 issues rose and 692 fell.
Eleven stocks hit a 52-week high while there was no new low; the Nasdaq Composite recorded 84 new highs and four new lows.