Tamweel shares rose the most in more than a week as the company prepared for a sukuk sale.
The Islamic mortgage provider's shares rose 0.8 per cent in early trading to Dh1.15 each.
Arranging banks told Reuters that the $235m sukuk, which is backed by residential mortgages, is due to be listed imminently on the Irish Stock Exchange.
But market traders seemed barely awake on trading floors around the country, with both emirates' markets practically unchanged after the first hour of trading.
The Dubai Financial Market General Index rose 0.1 per cent to 1,456.18, while the Abu Dhabi Securities Exchange General Index slipped 0.1 per cent to 2,478.23.
Arabtec Holding, Dubai Islamic Bank and Emaar Properties led gains on Dubai's market amid thin volumes.
In the capital, the National Bank of Abu Dhabi, Abu Dhabi Islamic Bank and Abu Dhabi National Energy Company, known as Taqa, made modest declines.
Most stocks were unchanged on both exchanges.
Asian markets rose on optimism that China could provide further economic stimulus and concerns about the eurozone sovereign debt crisis receded, with the Nikkei 225 gaining 0.7 per cent to 8,740.00 and the Hang Seng Index up 1.1 per cent at 19,209.00.
Oil prices fell, with Brent crude futures falling 42 cents to $92.63 per barrel and West Texas Intermediate crude down 32 cents to $79.11 per barrel.