Did you approach the company in person, which did not provide you with a relieving letter? This might be because, in some companies, HR department staff are ignorant about addressing the issues of ex-employees who call and request to resolve any grievances. Therefore, it is always advisable to go in person and request the concerned HR to issue a relieving letter by informing them that you have an opportunity to work in a multinational corporation (MNC) and that you might lose this chance without the letter. Generally, HR would consider such a request and would likely provide you with your relieving letter.
If the HR department is not issuing the letter despite repeated requests for various reasons, then meet with the unit head and explain your offer from the MNC and the response from the HR department in your case. If the unit head is cooperative, he will ask HR to issue the letter to you accordingly.
If even the unit head is unwilling to issue the letter, you should consider that they may have reservations about your attitude or performance. In such a scenario, there is no need to stress over it. Simply inform your new employer about your employment with the mentioned company, and request an exemption from submitting the relieving letter from that organization.
Regards