A deadline for Qatar to comply with a list of demands made by the states expired overnight. Doha has submitted replies to mediator Kuwait that have not been disclosed.
Doha has shown no sign of acquiescing to major demands, which raises the possibility of the four states imposing more sanctions. But it is not clear that any fresh steps - such as the withdrawal of deposits from Qatar's banking system - would be crippling, given Doha's large financial resources.
Qatar's index added 0.4 percent as 10 traded shares rose, including ones favoured by foreign funds such as Islamic lender Masraf Al Rayan, which added 1.0 percent.
Foreign funds were net buyers of Qatari stocks by a very narrow margin, bourse data showed; local funds were also net buyers, while Gulf funds were sellers. Twenty-seven stocks declined.
Saudi Arabia's index fell a further 0.5 percent, taking its losses over the last two sessions to 3.0 percent.
Second-quarter earnings announcements are due to start around mid-July, and Alrajhi Capital predicted in a note that consumer-related sectors would do well because of the reinstatement of civil servants' allowances and the month of Ramadan, which traditionally sees strong consumer spending.
Mobile phone and computer retailer United Electronics added 3.0 percent.
Earnings momentum for the broader market, however, is expected to be weak, according to a note by EFG Hermes. "Upside is limited for most of our coverage," it said, adding that it preferred banks over petrochemicals, and secular growth stories such as the insurance and supermarket industries.
In Dubai, builder Arabtec fell 1.2 percent on profit-taking to 3.19 dirhams. Earlier in the day it hit a high of 3.37 dirhams after announcing its subsidiary Target Engineering had been awarded four projects worth 289 million dirhams ($79 million).
Fifteen other shares fell and 11 advanced as the Dubai index closed near flat.
The banking sector helped take Abu Dhabi's index 0.5 percent higher with bellwether First Abu Dhabi Bank adding 1.0 percent.
In Cairo the blue-chip index closed near flat. The most heavily traded stock of the day was private equity firm Qalaa Holding, which jumped 6.9 percent.
Earlier this week its mining subsidiary ASEC Co for Mining reported that first-quarter net profit jumped to 232.4 million Egyptian pounds ($13.0 million) from a year-earlier loss 8.9 million pounds.
ASEC shares jumped 21 percent in the past two days but fell back 5.2 percent on Wednesday. The broader EGX100 index added 0.7 percent.