Titan said it would offer 2.5 shares for every Core share, valuing them at C42.2c, a 164% premium to its September 13 closing price.
Titan believes the acquisition will help it create "an emerging Latin American-focused gold explorer, developer and producer".
The offer will be open for 105 days and the Core board will advise of its recommendation in due course.
Core is currently undertaking a strategic review of alternatives, including equity or debt financings, core and non-core asset sales, strategic investments and joint ventures, as well as a potential merger with another company.
Titan had offered 20 shares for every Core share in February prior to a 10:1 share consolidation, valuing Core about C$72 million and representing a 44.7% premium to the previous trading day's close.
Titan's previous takeover attempt was thrown out in a landmark court decision in British Columbia in July on grounds the terms were not fair or reasonable.
A majority of Core shareholders had earlier voted in favour of the takeover but it was strongly opposed by Core's former CEO Keith Piggott, who had sought a separate C$100 million deal with Chinese gold producer Zhaojin and made allegations critical of Titan.
The offer will once again be put to a vote before Core shareholders, and remains subject to conditions.
Core shares trading in Toronto (TSXV:CGLD) closed up 9.3% at C23.5c on Tuesday to capitalise it at about $39 million (US$29.5 million).
Titan shares in Sydney (ASX:TTM) gained 2.8% or half-a-cent to A18.5c, capitalising it at $54.9 million (US$41.5 million).