Houthi rebels and loyalists of former president Ali Abdullah Saleh have been battling for control in Sanaa, which they jointly overran in 2014.
On Saturday, UAE Minister of State for Foreign Affairs Anwar Gargash said Qatar was seeking to mediate between warring rebels in Yemen.
"Qatar denies and strongly condemns statements by the UAE minister about Qatari mediation between Yemeni parties," a foreign ministry source said in statements carried by the official QNA news agency.
"Qatar welcomes any mediation to end this absurd war, for which the Yemeni people pay the price," the source said.
The UAE is a member of a Saudi-led coalition fighting Houthi rebels in Yemen since 2015.
Qatar has been under a blockade imposed by Saudi Arabia, the UAE, Egypt and Bahrain, who accuse Doha of supporting terrorism.
Qatar denies the accusations and contends that the blockade is in violation of international law.