* Oil prices fall about 2 pct
* GE boosts S&P
* Indexes up: Dow 0.19 pct, S&P 0.05 pct, Nasdaq 0.04 pct (Updates to open)
By Yashaswini Swamynathan
June 30 (Reuters) - A two-day rally by U.S. stocks faltered on Thursday as oil prices fell sharply and investors shifted their focus from Brexit to broader economic factors.
The three major indexes have recouped more than half of the losses suffered after a shock vote by Britain to leave the European Union. In a two-day panic selloff after the vote, global markets lost about $3 trillion in value.
Oil prices fell about 2 percent, snapping a two-day rally, as investors booked profits amid resumption of supply from Nigeria.
"The focus now shifts to reality and the performance of the global economy, which is not all that promising," said Peter Cardillo, chief market economist at First Standard Financial in New York.
Cardillo also noted that some traders would make adjustments to their portfolios as the quarter ends.
At 10:01 a.m. ET the Dow Jones industrial average was up 34.11 points, or 0.19 percent, at 17,728.79, the S&P 500 was up 1.09 points, or 0.05 percent, at 2,071.86 and the Nasdaq Composite was up 1.69 points, or 0.04 percent, at 4,780.94.
The three indexes had risen more than 1.5 percent in the past two days.
Data showed the number of Americans filing for unemployment benefits rose last week to 268,000, but remained below a level associated with a healthy labor market.
The weekly data is a precursor to the more comprehensive monthly payrolls report due next week, which is expected to feed into the U.S. Federal Reserve's decision on interest rate hikes this year.
Traders have priced in only a 13.4 percent chance of a hike as late as December, according to CME Group's FedWatch tool.
Eight of the 10 major S&P indexes were higher, with the industrials index's 0.52 percent rise leading the gainers.
General Electric rose 0.3 percent to $30.94 after Goldman Sachs raised its price target. GE provided the biggest boost to the S&P.
St. Louis president James Bullard is expected to speak on U.S. monetary policy outlook in London at 3:15 p.m. ET. Bullard's speech will be parsed for clues on whether the Fed has modified its forecasts after the Brexit vote.
ConAgra and Darden Restaurants fell more than 3 percent after reporting lower-than-expected quarterly sales.
Advancing issues outnumbered decliners on the NYSE by 1,405 to 1,345. On the Nasdaq, 1,241 issues rose and 1,146 .
The S&P 500 index showed 27 new 52-week highs and no new lows, while the Nasdaq recorded 26 new highs and 8 new lows. (Reporting by Yashaswini Swamynathan in Bengaluru; Editing by Saumyadeb Chakrabarty)