The Abu Dhabi Securities Exchange (ADX) gained 0.25 per cent to 2,711.30. Banking and telecommunication stocks posted gains but they were cancelled out by losses in the real estate and insurance sectors.
National Bank of Umm Al Quwain led gains, jumping 9.34 per cent to Dh1.99, and etisalat, the UAE's largest telco by market value, added 0.45 per cent to Dh11.15.
Aldar Properties, which accounted for a third of all trades, fell for a fifth consecutive day, dropping 2.4 per cent to Dh1.21.
"International issues are weighing on the bourse's performance," said Chahir Hosni, sales manager at EFG-Hermes.
Bank of Sharjah fell 0.52 per cent to Dh1.89, Sorouh Real Estate slipped 0.82 per cent to Dh1.19 and Methaq Takaful Insurance Company lost 4.17 per cent to Dh1.33.
The top loser was Oman and Emirates Investment Holding Company, which declined 9.41 per cent to Dh0.77 followed by Finance House, which fell 7.46 per cent to Dh3.6.
Of the 33 companies traded, eight rose, 16 fell and nine closed unchanged. Some 62.2 million shares worth Dh92.6 million were traded.
Elsewhere in the region, Saudi Arabia's Tadawul All Share Index rose 0.37 per cent to 6,531.17, Qatar's measure climbed 0.49 per cent, Kuwait's index slipped 0.43 per cent, Bahrain's bourse dropped 0.13 per cent and Muscat's exchange declined 0.8 per cent in Tuesday's trading.
The Dubai Financial Market (DFM) General Index fell to a 14 week low on Tuesday as international issues continue to take their toll on the bourse.
The DFM dropped 1.18 per cent to 1,507.61, its lowest close since March 21, with property and construction stocks suffering some of the biggest losses.
Bellwether Emaar Properties fell 2.31 per cent to a more than three month low of Dh2.96. The real estate developer announced on Tuesday that the head of its hospitality unit would be leaving the company.
Construction firm Arabtec dropped 1.57 per cent to Dh1.25 while ports operator DP World slipped 0.41 per cent to $12.15 on Nasdaq Dubai.
Global markets are anxiously awaiting the outcome of a vote in Greece to approve unpopular fiscal austerity measures.
Real estate stocks, however, are set to benefit from Tuesday afternoon's announcement by the Cabinet that three-year investor visas will be given to those investing in the UAE's real estate sector.
"The Cabinet's decision to grant three-year investor visas will have a real impact on the real estate market and we should see the DFM picking up from tomorrow [Wednesday]," said Chahir Hosni, sales manager at EFG-Hermes. .
"It is a very significant boost and will have an immediate impact on real estate stocks; it will create a wave of demand that was not there before," he added.