The German government said on Tuesday that it had concluded that Russia was responsible for the attempted drone attack last month.
Speaking ahead of an informal gathering of European foreign ministers in Ireland, Kallas also said that work is ongoing on 1600 sanctions listings related to Russia's military complex and "maybe there are more to be added".
Ministers arriving at the meeting said the bloc needs to look for more ways to put pressure on Moscow.
"I think we need to now really explore all the options on the table in terms of tightening the sanctions," Finnish Foreign Minister Elina Valtonen told reporters.
Lithuania's Foreign Minister Kestutis Budrys said Europeans need to consider their options and respond.
"It is obvious Russia does not see the political cost of its hybrid activities against us. So for them, this is the cheap way to make tensions in our society," he said, adding that "our goal is to show that these activities will neither intimidate us nor prevent us from supporting Ukraine and maintaining our pressure on Russia".
German Interior Minister Alexander Dobrindt said intelligence findings indicated that individuals involved in the attack were acting on behalf of Russian state agencies.
"Taken together, police investigations, patterns of the offences and intelligence findings establish Russian responsibility for the attempted attack at Leipzig Airport," he said.
Dobrindt said the technology found at the scene and the interplay of individual elements had to be described as professional, and indicated a high degree of technical expertise and considerable organisational effort in the planning and execution of the attack.
"The final execution of the attempted attack can be attributed to the area of low-level agents," he said, adding: "Let me make this clear: we are not at war but we are a daily target of hybrid warfare."
Standing alongside Dobrindt, Foreign Minister Johann Wadephul said Germany did not view Leipzig as an isolated incident.
"It fits into a broader pattern of Russian hybrid operations in Europe," he said.
A drone fitted with explosives and a detonation mechanism was discovered on the evening of August 4 in the security zone of Leipzig/Halle Airport, between Ukrainian cargo aircraft, prompting a temporary halt to flights.
In response to the attack, Wadephul said on Tuesday Germany would take a series of measures including closing Russia's consulate general in Bonn and terminating its agreement with the Russian House cultural centre in Berlin.
"Germany remains secure, and Germany will defend itself against adversaries who seek to create insecurity," Wadephul said.
"We will not allow Russia's attacks to divide or intimidate us in our social cohesion."
Germany will also push within the European Union for additional sanctions listings and travel restrictions on Russian citizens while increasing pressure on Russia's "shadow fleet," he said.
Responding to Germany's announcement, Russian foreign ministry spokeswoman Maria Zakharova said her country would respond to what she called Germany's "anti-Russian action," according to Interfax news agency.
Russia would respond "in kind" to any new German sanctions, Zakharova told the DPA news agency.
The Russian embassy in Berlin had previously dismissed such accusations as "fabricated provocation" and as "a new wave of anti-Russian hysteria in Germany".
with DPA and AP
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