Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani said Qatar had not yet been presented with a list of demands by countries that cut off diplomatic and transport ties, but insisted the matter be solved peacefully.
And the Emirates Post Group said that it had stopped all types of postal services to Qatar despite the UAE's continued diplomatic relations with Iran.
The Saudi newspaper al Watan published what it called a list of eight "extremist organisations" seen as working to destabilise the region from Qatar, including Qatar's Al Jazeera news channel, that were targeted by Gulf Arab states.
Bahrain's move against Qatar is in step with other members of the Gulf Cooperation Council, a close regional alliance that includes Saudi Arabia, the UAE, Oman, Kuwait and Qatar.
As the Gulf crisis deepened with four major Arab nations closing sea, air and land links with Qatar, India is beginning to worry about its over 6,30,000 nationals living in that country.
Trump had accused Qatar of supporting terrorism in a series of tweets on Tuesday.
Turkey, which works closely with Qatar in the energy sector, has walked a fine line between defending Qatar and abstaining from openly antagonising Saudi Arabia.
In this February 6, 2012 photo, then-Emir of Qatar, Sheikh Hamad Bin Khalifa Al-Thani, center, Palestinian President Mahmoud Abbas, left, and then-Hamas leader, Khaled Mashaal, arrive to sign an agreement in Doha, Qatar.
Kuwait's emir is working to mediate the Gulf crisis around Qatar, which is home to a major USA military base and is the host of the 2022 FIFA World Cup.
Ankara hosted Iranian Foreign Minister Mohammad Javad Zarif this week for talks, including on Qatar.
Qatar and Iran already share a gas field in the Persian Gulf.
Doha has for years forged its own alliances in the region, often diverging from the politics of the six-state GCC and taking in leaders of the Muslim Brotherhood, the Palestinian Hamas and members of the Afghan Taliban.
A top United Arab Emirates official on Wednesday told AFP that the unprecedented measures were aimed at pressuring Doha into making drastic policy changes.
"This is not about regime change - this is about change of policy, change of approach", said Anwar Gargash, the UAE state minister for foreign affairs.
"The previous emir is a big supporter of this whole extremist agenda, so we do have an issue", the official said. Analysts say President Donald Trump's recent visit to Saudi Arabia, during which the leader condemned Iran as the world's most prolific state-sponsor of terrorism, fueled an increase in political capital for the hardline anti-Tehran factions in Riyadh.
Officials from Qatar and its Gulf Arab neighbors embarked on a quickening round of shuttle diplomacy, with the Qatari foreign minister due in Moscow and Brussels and Bahrain's king visiting his ally Egypt for talks on the crisis.
Bahrain on Thursday followed the UAE in announcing that expressing sympathy for Qatar over the sanctions was an offence punishable by jail.