"There is this historic opportunity to occupy the space of the anti-Left feeling and our long-term strategy will be towards that," Jaitley, who came here to attend the swearing-in ceremony of the Mamata Banerjee-led government, said.
"This time it is a hat-trick of anti-Left voting. No doubt in our mind that our primary objective in the long run is to occupy the space of the Left and become principal opposition party in the state. The footprint has been registered by us," he said.
In the just-concluded state Assembly polls, the BJP secured three seats while the GJM, which had supported the BJP in the 2014 Lok Sabha election, secured three seats.
In the 2011 Assembly polls, the BJP failed to secure any seat but in a by-election thereafter it won a seat.
Jaitley described his party's inroads into the Left dominated states of West Bengal and Kerala as a "success story" and asserted that it was spreading fast into the parts of the country where it had no presence in the past.
He said that soon it would be a tripolar contest in Kerala.
In Bengal, he said, the BJP got 10.8% votes and received considerable voter support in 200 seats, which he described as a "healthy trend".
Replying to a query on his attending the oath-taking ceremony of Mamata Banerjee when his party's state unit colleagues boycotted it, Jaitley said the federal structure of the country has to be respected.
He made it clear that in accordance with the obligations of the federal structure of the Constitution, the Centre would continue to support West Bengal when it came to clearing any project or for any other support under the government-to-government relationship.
However, there was no scope of an out-of-turn fiscal assistance for West Bengal, which Chief Minister Mamata Banerjee had repeatedly sought in the past.
"All funding is tied up under the 14th Finance Commission and if there is any lacunae in what is entitled to the state then it must be pointed out in specific," Jaitley pointed out.
On the call for the formation of a federal front by certain political parties, Jaitley said it had "failed" in the past.
"We will welcome anybody coming in opposition to the BJP. The alternative alliance should have a stable anchor with a national presence. The past experience of the failure of federal fronts was because the anchor was narrow in support.
"Any alliance which is anchored by small groups will never be stable. The last example was that of the United Front 20 years back," Jaitley said.
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