A gunman broadcast live footage on Facebook of the attack on one of the mosques, showing him driving to the scene, entering the building and shooting people at random.
One of the men in his late 20s has been charged with murder and is due in court on Saturday.
Basu said British counter-terror officers were ready to support their colleagues in New Zealand in responding to and investigating Friday's attack.
"An attack against peaceful people gathering for prayer is shocking in its cruelty and cynicism", Russian President Vladimir Putin said.
The attacks took place at two mosques: the Masjid Al-Noor Mosque near Hagley Park and Linwood Masjid Mosque in Christchurch. Peneha said he saw the attacker flee the mosque and then drop his semi-automatic weapon in his driveway.
She added: "It is clear that this can now only be described as a terrorist attack".
British security sources said there were no apparent United Kingdom links to the attack. The gunman spends more than two minutes inside the Al-Noor mosque firing indiscriminately at men, women and children from close range.
All mosques in New Zealand had been asked to shut their doors and armed guards posted at them, police said, adding they were not actively looking for any other "identified suspects".
Dr Hartley said that New Zealand "gives room for diversity, and prides itself on that: it prides itself on being a place where people can be welcomed".
One of the gunmen - believed to be an Australian extremist - livestreamed the deadly assault, stoking outrage and fear that others may be targeted in copy-cat attacks.
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Britain's Queen Elizabeth said she was "deeply saddened by the appalling events in Christchurch today". He wrote, "I only arrived to New Zealand to live temporarily whilst I planned and trained, but I soon found out that New Zealand was as target rich of an environment as anywhere else in the West".
"Together with our intelligence partners we continually monitor the varied threats we face, including to and around places of worship and specific communities across the country", he said.
"We will and must reject it".
Bury St Edmunds MP Jo Churchill Tweeted on Friday morning: "Our condolences to the people of Christchurch New Zealand".
Dr Mohammad Faisal, spokesman for Pakistan's Ministry of Foreign Affairs, wrote on Twitter that his country "condemns the tragic terrorist incident" and said the High Commission for Pakistan is in touch with New Zealand's authorities to obtain details about the victims. "Prince Philip and I send our condolences to the families and friends of those who have lost their lives".
Traini's lawyer Gianluca Giulianelli said on the radio that his client had repented and "firmly dissociates himself" from the New Zealand killer.
Tamim Iqbal tweeted: "Entire team got saved from active shooters!"
London Mayor Sadiq Khan said there will be a "highly visible" policing presence around the capital's mosques today as he sought to offer reassurance to those heading to Friday prayers.
Police urged both the media and public to "show restraint" and not share it.
"I can confirm that the individual who was taken into custody I have been advised is an Australian-born citizen", Morrison told reporters in Sydney on Friday.