*507Plaintiffs Yoda and Riverhead, the general contractor and owner of a construction site, seek coverage under an excess insurance policy issued by defendant National Union to their subcontractor, Queens Stainless, with respect to the underlying Labor Law action. Their insurer, plaintiff United National, seeks a declaration that its coverage follows that of National Union.
The National Union excess policy follows the form of a commercial general liability policy, issued by First Specialty to Queens Stainless, that provides coverage to its insured for damages arising from bodily injury, and excludes coverage for liability arising from a contractual “agreement,” except if the insured has assumed liability for such damages under an “insured contract,” such as the subcontract between Yoda and Queens Stainless. The First Specialty policy also provides that its employer’s liability exclusion “does not apply to liability assumed by the insured under an ‘insured contract,’ ” and requires the insurer to defend an indemnitee of the insured in certain circumstances.
In 2003, Yoda tendered the defense and indemnity in the underlying action to Queens Stainless and its insurers, and First Specialty accepted the tender, although no action for indemnification had been commenced against Queens Stainless. National Union actively participated in and monitored the litigation for the next three years, without issuing any disclaimer. In 2006, it accepted First Specialty’s tender of its policy in connection with a court-ordered mediation, and attended the mediation with authority to settle the underlying action. Only after partial summary judgment was awarded in favor of the plaintiffs in the underlying action, and the damages trial was scheduled to begin, did National Union disclaim coverage, asserting that it had just “discovered” that the certificate of insurance provided to it by Yoda, which names Yoda and Riverhead as additional insureds, was false.
National Union’s failure to timely disclaim coverage after tender was made by a party claiming indemnification from its insured, as required by Insurance Law § 3420 (d), precludes it from disclaiming based on the employer’s liability exclusion. However, the failure to disclaim “does not create coverage which *508the policy was not written to provide” (Zappone v Home Ins. Co., 55 NY2d 131, 134 [1982]; National Abatement Corp. v National Union Fire Ins. Co. of Pittsburgh, Pa., 33 AD3d 570, 571 [2006]). The First Specialty policy does not provide automatic additional insured coverage for parties indemnified under an “insured contract” (compare Kassis v Ohio Cas. Ins. Co., 12 NY3d 595 [2009]). However, in convoluted fashion, it provides “insured contract” coverage to the named insured through an exception to an exclusion (see 17A Couch on Insurance 3d § 254:13). Even were we to find that the policy is ambiguous, the issue of the parties’ intent is one of fact not resolved by the extrinsic evidence in this record (see Katz v American Mayflower Life Ins. Co. of N.Y., 14 AD3d 195, 207-208 [2004], affd 5 NY3d 561 [2005]).
Although Insurance Law § 3420 (d) does not create coverage, an insurance company may be estopped “from denying or disclaiming coverage where the proper defending party relied to its detriment on that coverage and was prejudiced by the delay of the insurance company in denying or disclaiming coverage based on the loss of the right to control its own defense” (Liberty Ins. Underwriters, Inc. v Arch Ins. Co., 61 AD3d 482, 482 [2009] [internal quotation marks and citation omitted]; Federated Dept. Stores, Inc. v Twin City Fire Ins. Co., 28 AD3d 32, 38 [2006]). The doctrine may be applied in disputes between insurers (see Liberty Ins. Underwriters, 61 AD3d at 482). However, “[prejudice is established only where the insurer’s control of the defense is such that the character and strategy of the lawsuit can no longer be altered” (Federated Dept. Stores, 28 AD3d at 39).
In support of their motion for summary judgment, plaintiffs submitted evidence that National Union acknowledged coverage in correspondence and actively participated in the defense, culminating in its lead role in the mediation, and that plaintiffs had been prejudiced in the defense of the underlying action. If National Union had disputed coverage in a reasonably timely manner, plaintiffs could have impleaded Queens Stainless, thereby triggering insured contract coverage or, at least, timely resolution of any disclaimer. Plaintiff United National asserts that it relied on National Union’s conduct and allowed its file to become inactive, believing that the matter would settle within the limits of the insurance provided by Queens Stainless’s insurers. In opposition, National Union claimed that it had been misled by Yoda’s tender of a certificate of insurance showing coverage. However, there is no evidence that Yoda acted in bad faith, and nothing prevented National Union from obtaining a copy of *509the primary policy during the three years following the tender (see Utica Mut. Ins. Co. v 215 W. 91st St. Corp., 283 AD2d 421 [2001]; compare Federated Dept. Stores, 28 AD3d at 34-35 [purported insured failed to comply with insurer’s requests for a copy of its contract with the insured, which would trigger “insured contract” coverage]). In the absence of any material issues of fact, National Union is estopped from denying that it provides excess coverage for Yoda and Riverhead in the underlying action. However, United National is not entitled to summary judgment against National Union on the issue of priority of coverage inasmuch as issues of fact exist as to whether United National reasonably relied to its detriment on National Union’s conduct. Concur — Saxe, J.E, Friedman, Abdus-Salaam and Román, JJ.