Valeant on Wednesday offered to pay $58.30 per Allergan share in cash, about $10 higher than its previous offer of $48.30. The stock component of the offer remains the same at 0.83 of a Valeant share for each Allergan share.
Valeant Chief Executive Michael Pearson admitted at a meeting Wednesday that "being engaged with Allergan is a bit of a pastime," but stressed that his company is "committed to not overpaying."
Still, Pearson said he fully expects that in the end, the company will merge with Allergan.
The new offer values Allergan at $166.16 per share as of Tuesday's closing price, and is about 8.6 percent higher than the previous bid of $153 as on April 22 when Valeant first made its offer.
Read More Allergan rejects Valeant Pharma's 'cut and slash' takeover
That offer, by Valeant and activist investor Bill Ackman, was worth $47 billion and was spurned by Allergan, which said the Canadian company had overstated possible savings from the deal.
Valeant's pursuit of Allergan comes during one of the busiest periods for M&A in the pharmaceutical sector.
Valeant's offer on Wednesday is lower than $180-$200 per share that investors were looking for, according to an investor survey last week.
Read More I did not front-run Allergan stock, Ackman says
But the new offer also includes a contingent value right of up to $25 per share related to the sales of Darpin, Allergan's experimental eye drug that is seen as a potential competitor to Regeneron Pharmaceuticals's successful medicine Eylea. The potential value of the Darpin contingent value right was not immediately available.
"Allergan shareholders want this deal to occur, but they want a higher price and the optionality on Darpin," Pearson said to about 300 shareholders of the two companies. "We think the offer we made this morning addresses both of those concerns."
As for Valeant's interest in the proposed deal, Pearson said his company does not care about "getting bigger," only creating value for its shareholders.