Mass interception of online communications by intelligence agencies is necessary – even if only one person is being targeted, lawyers for the government have told a tribunal hearing complaints about surveillance.

The government's arguments were disclosed as lawyers for Liberty and otherright organisations told the investigatory powers tribunal (IPT) safeguards surrounding GCHQ's collection online data are inadequate and do not conform to the law.

The groundbreaking case against GCHQ and the government is the result of revelations by the US whistleblower Edward Snowden. It has been brought by Privacy International, Liberty, Amnesty International, the American Civil Liberties Union and other overseas human rights groups.

In an 85-page written argument released at the IPT, government lawyers cite the example of the intelligence agencies needing to obtain communications being sent to a suspect in Syria.

"For nearly all forms of internet-based communication, the only way to intercept those [messages] being sent [to the suspect] is to intercept a substantially greater volume of communications (including, potentially, a volume of internal communications) and then apply a selection stage to identify the communications in question.

"... Unless the [civil liberties groups] wish to submit that the intelligence services should not be able to obtain the external communications that are needed for the purposes of national security etc, they must accept some form of interception regime that permits substantially more communications to be intercepted (including potentially internal communications) than are actually being sought."

But Matthew Ryder QC, for Liberty and other human rights groups, told the tribunal: "Our challenge is against the legal framework which we say is inadequate and not in accordance with the law.

"Tempora is a UK alleged government programme [which] involves the collection of vast amounts of information flowing through fibre-optic cables ... It may be that [the government has] crossed a Rubicon and decided that [mass] data-gathering exercises are something [it] should try out – but you can't have it under the existing regime."

Ryder said the regulations under which interceptions are carried out did not tell the public that carrying out an online search on Google – often using a foreign server overseas and therefore deeemed to be an "external communication" – could make them the subject of official surveillance without an individual warrant being obtained.

Liberty's submission to the tribunal warns that "the US government's collection of personal communications and related data from US communication service providers is carried out on a vast scale" and any information obtained by the US "is likely to be shared extensively between US and UK agencies".

A written submission to the tribunal from Privacy International asks whether it is right "that the government can issue a general warrant for the universal search, seizure and sophisticated automatic analysis of communications and their sharing with foreign governments.

"[The case] is also about the government's ability to obtain virtually all communications of UK residents from the intelligence services of other states without requiring any warrant at all and subject only to a general power to act 'in the interests of national security'."

The legal challenge is the first of dozens of GCHQ-related claims to be examined in detail by the IPT, which hears complaints against British intelligence agencies and government bodies that carry out surveillance under the Regulation of Investigatory Powers Act (Ripa).

The civil liberties organisations are concerned that their private communications have been monitored under Tempora, whose existence was revealed by Snowden. They also complain that information obtained through the NSA's Prism and upstream programmes may have been shared with the British intelligence services, sidestepping protections provided by the UK legal system.

The chairman of the tribunal, Mr Justice Burton, asked lawyers for the government whether intelligence-sharing with the United States – where information was intercepted overseas by foreign agencies – complied with the right to privacy and family life under article 8 of the European convention on human rights.

James Eadie QC, for the government, said he believed the process was compliant with the convention but sought time for further clarification.

Burton said the IPT was unusual in hearing evidence on the basis of assumed facts. "The whole shooting match is being assumed for the purpose of today," he added.

Written submissions for the government accept that under the "alleged" Tempora operation, "the claimants' [the civil liberty organisations'] communications might in principle have been intercepted in the UK … and at least some of those intercepted communications might in principle have been read, looked at or listened [to]."

There are four other members of the tribunal, along with Burton: Robert Seabrook QC, Christopher Gardner QC, chief justice of the British Indian Ocean Territory, Geoffrey Rivlin QC and Mrs Justice Carr, a high court judge. The hearing is expected to last all week.