DUBAI, July 4 (Reuters) - Qatar's stock market continued rebounding early on Tuesday from lows hit because of the diplomatic crisis surrounding Doha, while profit-taking in a few Saudi Arabian blue chips dragged down that market.

A deadline set by four Arab states for Doha to comply with their demands will expire late on Tuesday, and recent comments by Qatari officials suggest it is unlikely to acquiesce to enough of the demands to avoid further economic sanctions.

But net buying by foreign investors in the Qatari stock market over the last few days suggests some funds do not think the additional sanctions would be crippling, while they believe there is now value in the market.

Qatar's stock index, which had rebounded 1.3 percent on Monday, added a further 1.1 percent in early trade on Tuesday. Some blue chips remained weak, with Qatar National Bank down 0.2 percent, for example.

But companies linked to Qatari gas production were strong as the chief executive of Qatar Petroleum outlined plans to raise output and capacity in coming years.

Gulf International Services, the most heavily traded stock, surged 4.0 percent and Qatar Gas Transport soared its 10 percent daily limit.

Saudi Arabia's index fell 0.5 percent as a few blue chips, which had surged last week after MSCI said it would consider Riyadh for emerging market status and economic reformer Mohammed bin Salman was promoted to crown prince, pulled back.

National Commercial Bank, the largest lender, was the biggest loser, dropping 3.1 percent. Miner Ma'aden slipped 0.6 percent.

Second- or third-tier stocks accounted for much activity and some rose strongly; Wafa Insurance gained 5.3 percent after the central bank said it would let the company accept new subscribers in vehicle insurance, lifting a suspension on this activity.

Dubai's index fell 0.5 percent as blue chip Emaar Properties slid 1.1 percent. But GFH Financial , the most heavily traded stock, rose 1.8 percent after saying it had obtained approval from the central bank of Bahrain to buy back up to 5 percent of its issued treasury shares.

Builder Arabtec surged 4.1 percent after saying it had won a 353 million dirham ($96 million) contract from to build the United Arab Emirates pavilion at Expo 2020 world's fair in Dubai. (Reporting by Andrew Torchia; Editing by Richard Balmforth)